
Advances in HighPerformance Sparse Matrix Computation (4 talks)
Mathias Jacquelin, Esmond Ng
Summary: This minisymposium will focus on advances in the solution of sparse systems of linear equations. We will consider both recent work in direct methods and iterative methods, with an emphasis on performance and scalability on current and future computer architectures. We will also discuss the roles of such solvers in the solution of largescale scientific problems.
 Towards highly scalable asynchronous sparse solvers for symmetric matrices
Mathias Jacquelin
 Finegrained Parallel Incomplete LU Factorization
Edmond Chow
 Approximate sparse matrix factorization using lowrank compression
Pieter Ghysels
 Hiding latencies and avoid communications in Krylov solvers
Wim Vanroose

Advances in preconditioning and iterative methods (4 talks)
Jennifer Pestana, Alison Ramage
As mathematical models become increasingly complex, efficiently solving large sparse linear systems remains a key concern in many applications. Iterative solvers are often the method of choice, in which case effective preconditioners are usually required. In this minisymposium, speakers will present recent advances in iterative methods and preconditioners.
 Symmetrizing nonsymmetric Toeplitz matrices in fractional diffusion problems
Jennifer Pestana
 An Approximate InverseBased Preconditioner for Incompressible Magnetohydrodynamics
Michael Wathen
 Commutator Based Preconditioning for Incompressible TwoPhase Flow
Niall Bootland
 The efficient solution of linear algebra subproblems arising in optimization methods
Tyrone Rees

Asynchronous Iterative Methods in Numerical Linear Algebra and Optimization (4 talks)
Hartwig Anzt, Edmond Chow, Daniel B. Szyld
In asynchronous iterative methods, a processing unit that normally depends on the datacomputed by other processing units is allowed to proceed even if not all theseother processing units have completed their computations. Originally calledChaotic Relaxation for fixedpoint iterations, asynchronous iterative methods havealso now been developed for numerical optimization. In this minisymposium, recent research is presented both on the theoryand implementation of asynchronous iterative methods.
 ARock: Asynchronous Parallel Coordinate Updates
Ming Yan
 Asynchronous Domain Decomposition Solvers
Christian Glusa
 Asynchronous Linear System Solvers on Supercomputers
Teodor Nikolov
 Asynchronous Optimized Schwarz Methods for Poisson's Equation in Rectangular Domains
José Garay

Constrained LowRank Matrix and Tensor Approximations (8 talks)
Grey Ballard, Ramakrishnan Kannan, Haesun Park
Constrained low rank matrix and tensor approximations are extremely useful in largescale data analytics with applications across data mining, signal processing, statistics, and machine learning. Tensors are multidimensional arrays, or generalizations of matrices to more than two dimensions. The talks in this minisymposium will span various matrix and tensor decompositions and discuss applications and algorithms, as well as available software, with a particular focus on computing solutions that satisfy applicationdependent constraints.
 Constrained Low Rank Approximations for Scalable Data Analytics
Haesun Park
 Tensor decompositions for big multiaspect data analytics
Evangelos Papalexakis
 Speeding Up Tensor Contractions through Extended BLAS Kernels
Animashree Anandkumar
 Scalable & Constrained PARAFAC2 for Sparse Data
Ioakeim Perros
 PLANC: Software for Parallel Lowrank Approximation with Nonnegative Constraints
Ramakrishnan Kannan
 Efficient CPALS and Reconstruction from CP Form
Jed Deursch
 Nonnegative Sparse Tensor Decomposition on Distributed Systems
Jiajia Li
 CommunicationOptimal Algorithms for CP Decompositions of Dense Tensors
Grey Ballard

Coupled matrix and tensor decompositions: Theory and methods (3 talks)
Dana Lahat
Matrices and higherorder arrays, also known as tensors, are natural structures for data representation, and their factorizations in lowrank terms are fundamental tools in data analysis. In recent years, there has been increasing interest in more elaborate data structures and coupled decompositions that provide more efficient ways to exploit the various types of diversity and structure in a single dataset or in an ensemble of possibly heterogeneous linked datasets. Such data arise in multidimensional harmonic retrieval, biomedical signal processing, and social network analysis, to name a few. However, understanding these new types of decompositions necessitates the development of new analytical and computational tools.
In this minisymposium, we present several different frameworks that provide new insights into some of these types of coupled matrix and tensor decompositions. We show how the concept of irreducibility, borrowed from representation theory, is related to the uniqueness of coupled decompositions in lowrank terms, as well as to coupled Sylvestertype matrix equations. We compare the gain that can be achieved from computing coupled CP decompositions of tensors in a semialgebraic framework, in several scenarios. Finally, we study connections between different tensorization approaches that are based on decoupling multivariate polynomials.
We discuss advantages and drawbacks of these approaches, as well as their potential applications.
 Understanding the uniqueness of decompositions in lowrank block terms using Schur's lemma on irreducible representations
Dana Lahat
 What can we gain from coupled SECSI in the rank 2 case? An analytical firstorder performance analysis
Yao Cheng
 Decoupling multivariate polynomials: comparing different tensorization methods
Philippe Dreesen

Discovery from Data (12 talks)
Theodore E. Schomay, Katherine A. Aiello, Sri Priya Ponnapalli, Orly Alter
The number of largescale highdimensional datasets recording different aspects of interrelated phenomena is growing, accompanied by a need for mathematical frameworks for discovery from data arranged in structures more complex than that of a single matrix. In the three sessions of this minisymposium we will present recent studies demonstrating ``Discovery from Data,'' in ``I: Systems Biology,'' and ``II: Personalized Medicine,'' by developing and using the mathematics of ``III: Tensors.''
 Patterns of DNA CopyNumber Alterations Revealed by the GSVD and Tensor GSVD Encode for Cell Transformation and Predict Survival and Response to Platinum in Adenocarcinomas
Sri Priya Ponnapalli
 Systems Biology of Drug Resistance in Cancer
Antti Hakkinen
 SingleCell Entropy for Estimating Differentiation Potency in Waddington's Epigenetic Landscape
Andrew E. Teschendorff
 Dimension Reduction for the Integrative Analysis of Multilevel Omics Data
Gerhard G. Thallinger
 Mathematically Universal and Biologically Consistent Astrocytoma Genotype Encodes for Transformation and Predicts Survival Phenotype
Katherine A. Aiello
 Statistical Methods for Integrative Clustering Analysis of MultiOmics Data
Qianxing Mo
 Structured Convex Optimization Method for Orthogonal Nonnegative Matrix Factorization with Applications to Gene Expression Data
Junjun Pan
 Mining the ECG Using Low Rank Tensor Approximations with Applications in Cardiac Monitoring
Sabine Van Huffel
 Tensor HigherOrder GSVD: A Comparative Spectral Decomposition of Multiple ColumnMatched but RowIndependent LargeScale HighDimensional Datasets
Theodore E. Schomay
 The GSVD: Where are the Ellipses?
Alan Edelman
 Tensor convolutional neural networks (tCNN): Improved featurization using highdimensional frameworks
Elizabeth Newman
 Threeway Generalized Canonical Correlation Analysis
Arthur Tenenhaus

Domain decomposition methods for heterogeneous and largescale problems (8 talks)
Eric Chung, Hyea Hyun Kim
Many applications involve the solutions of coupled heterogeneous systems,and the resulting discretizations give huge linear or nonlinear systems of equations,which are in general expensive to compute. One popular and efficient approach is the domain decomposition method.While the method is successful for many problems, there are still many challenges inthe application of the domain decomposition method for heterogeneous and multiscale problems. In this minisymposium, we will review some recent advances in the use of domain decomposition and related methodsto solve complex heterogeneous and largescale problems.
 Fast solvers for multiscale problems
Hyea Hyun Kim
 SpaceTime Schwarz Preconditioning and Applications
Xiaochuan Cai
 Robust BDDC and FETIDP methods in PETSc
Stefano Zampini
 A GMsFEM based domain decomposition method for linear elasticity in high contrast media
Yanfang Yang
 A Parareal Algorithm for Coupled Systems Arising from Optimal Control Problems
Felix Kwok
 Convergence of Adaptive Weak Galerkin Finite Element Methods
Liuqiang Zhong
 A nonoverlapping DD method for an interior penalty method
EunHee Park
 A twogrid preconditioner for flow simulations in highly heterogeneous media with an adaptive coarse space
Shubin Fu

Efficient Kernel Methods and Numerical Linear Algebra (8 talks)
Evgeny Burnaev, Ivan Oseledets
Summary: Despite their theoretical appeal and grounding in tractable convex optimization techniques, kernel methods are often not the first choice for largescale machine learning applications due to their significant memory requirements and computational expense.
Thus it is not surprising that mainly due to the advances of deep learning, the performances in various machine learning tasks have been progressing intensively. However, in recent years different elegant mechanisms (such as randomized approximate feature maps) to scaleup kernel methods emerged mainly from computational mathematics and applied linear algebra. So these are indications that kernel methods are not dead and that they could match or even outperform deep nets.
To tackle such challenging area, one appeals for new advanced approaches at the bridge of numerical linear algebra and kernels methods. Therefore, the purpose of the minisymposium is to bring together experts in modern machine learning and scientific computing to discuss current results in numerical approximation and its usage for scaling up kernel methods, as well as potential areas of application. The emphasis is put on original theoretical and algorithmic developments, however interesting application results are welcome as well.
 Overview of Large Scale Kernel Methods
Evgeny Burnaev
 Kernel Methods and Tensor Decompositions
Ivan Oseledets
 Quadraturebased features for kernel approximation
Ermek Kapushev
 Convergence Analysis of Deterministic Kernelbased Quadrature Rules in Sobolev Spaces
Motonobu Kanagawa
 Sequential Sampling for Kernel Matrix Approximation and Online Learning
Michal Valko
 Tradeoffs of Stochastic Approximation in Hilbert Spaces
Aymeric Dieuleveut
 Deep Kernel Learning and Structured Kernel Interpolation
Andrew Gordon Wilson
 Kernel Methods for Causal Inference
Krikamol Muandet

Exploiting LowComplexity Structures in Data Analysis: Theory and Algorithms (8 talks)
Ju Sun, Ke Wei
Summary: Lowcomplexity structures are central to modern data analysis  they are exploited to tame data dimensionality, to rescue illposed problems, and to ease and speed up hard numerical computation. In this line, the past decade features remarkable advances in theory and practice of estimating sparse vectors or lowrank matrices from few linear measurements. Looking ahead, there are numerous fundamental problems in data analysis coming with more complex data formation processes. For example, the dictionary learning and the blind deconvolution problems have intrinsic bilinear structures, whereas the phase retrieval problem and variants pertain to quadratic measurements. Moreover, many of these applications can be naturally formulated as nonconvex optimization problems, which are ruled to be hard by the worstcase theory. In practice, however, simple numerical methods are surprisingly effective in solving them. Partial explanation of this curious gap has started to appear very recently.
This minisymposium highlights the intersection between numerical linear algebra/numerical optimization and the mathematics of modern signal processing and data analysis. Novel results on both theoretical and algorithmic sides of exploiting lowcomplexity structures will be discussed, with an emphasis on addressing the new challenges.
 When Are Nonconvex Optimization Problems Not Scary?
Ju Sun
 The Scaling Limit of Online Lasso, Sparse PCA and Related Algorithms
Yue M. Lu
 Accelerated Alternating Projection for Robust Principle Component Analysis
JianFeng Cai
 Numerical integrators for rankconstrained differential equations
Bart Vandereycken
 Foundations of Nonconvex and Nonsmooth Robust Subspace Recovery
Tyler Maunu
 Geometry and Algorithm for Sparse Blind Deconvolution
Yuqian Zhang
 Convergence of the randomized Kaczmarz method for phase retrieval
Halyun Jeong
 Nonconvex Optimization for Highdimensional Learning
Mahdi Soltanolkotabi

Generalized Inverses and the Linear Least Squares (8 talks)
Dragana Cvetkovic Ilic, Ken Hayami, Yimin Wei
Summary: Within this minisymposium we will consider some actual problems of the generalized inverses, generalized invertibility of operators, representations of the Drazin inverse, least squares problem, and computing generalized inverses using gradient neural networks and using database stored procedures. We will develop the relationship between generalized inverses and the linear least squares problem with applications in signal processing.
 Recovery of sparse integervalued signals
XiaoWen Chang
 Various properties of operator matrices and its different applications
Dragana Cvetkovic Ilic
 Computing timevarying MLweighted pseudoinverse by the Zhang neural networks
Sanzheng Qiao
 GNN and ZNN solutions of linear matrix equations
Predrag S. Stanimirović
 Randomized Algorithms forTotal Least Squares Problems
Hua Xiang
 Randomized Algorithms for Core Problem and TLS problem
Liping Zhang
 Condition Numbers of the Multidimensional Total Least Squares Problem
Bing Zheng
 Fast solution of nonnegative matrix factorization via a matrixbased active set method
Ning Zheng

Iterative Solvers for ParallelinTime Integration (4 talks)
XiaoChuan Cai, Hans De Sterck
Due to stagnating processor speeds and increasing core counts, the current paradigm of high performance computing is to achieve shorter computing times by increasing the concurrency of computations. Sequential timestepping is a computational bottleneck when attempting to implement highly concurrent algorithms, thus parallelintime methods are desirable. This minisymposium will present recent advances in iterative solvers for parallelintime integration. This includes methods like parareal, multigrid reduction, and parallel spacetime methods, with application to linear and nonlinear PDEs of parabolic and hyperbolic type.
 SpaceTime Schwarz Preconditioning and Applications
XiaoChuan Cai
 ParallelinTime Multigrid with Adaptive Spatial Coarsening for the Linear Advection and Inviscid Burgers Equations
Hans De Sterck
 On the convergence of PFASST
Matthias Bolten
 Waveform Relaxation with Adaptive Pipelining (WRAP)
Felix Kwok

Largescale eigenvalue problems and applications (11 talks)
Haizhao Yang, Yingzhou Li
Eigenvalue problem is the essential part and the computationally intensivepart in many applications in a variety of areas, including, electronstructure calculation, dynamic systems, machine learning, etc. In all theseareas, efficient algorithms for solving largescale eigenvalue problems aredemanding. Recently many novel scalable eigensolvers were developed to meetthis demand. The choice of an eigensolver highly depends on the properties and structure of the application. Thisminisymposium invites eigensolver developers to discuss the applicabilityand performance of their new solvers. The ultimate goal is to assistcomputational specialists with the proper choice of eigensolvers fortheir applications.
 Interior Eigensolver for Sparse Hermitian Definite Matrices Based on Zolotarev's Functions
Haizhao Yang
 The ELSI Infrastructure for LargeScale Electronic Structure Theory
Volker Blum
 Recent Progress on Solving Largescale Eigenvalue Problems in ElectronicStructure Calculations
Chao Yang
 Polynomial and rational filtering, spectrum slicing and EVSL package
Yuanzhe Xi
 The Full Configuration Interaction Quantum Monte Carlo(FCIQMC) in the lens of inexact power iteration
Zhe Wang
 A FEAST Algorithm with oblique projection for generalized eigenvalue problems
Guojian Yin
 Real eigenvalues in linear viscoelastic oscillators
Heinrich Voss
 Error bounds for Ritz vectors and approximate singular vectors
Yuji Nakatsukasa
 Consistent symmetric greedy coordinate descent method
Yingzhou Li
 On the accuracy of fast structured eigenvalue solutions
Jimmy Vogel
 Generation of large sparse test matrices to aid the development of largescale eigensolvers
Peter Tang

Largescale matrix and tensor optimization (4 talks)
Yangyang Xu
Summary: Matrix and tensor optimization problems naturally arise from applications that involve twodimensional or multidimensional array data, such as social network analysis, neuroimaging, Netflix recommendation system, and so on. Unfolding the matrix and tensor variable and/or data into a vector may lose the intrinsic structure. Hence it is significant to keep the matrix and tensor format. This minisymposium includes talks about recently proposed models and algorithms with complexity analysis for largescale matrix and tensor optimization.
 Greedy method for orthogonal tensor decomposition
Yangyang Xu
 Second Order Sparsity and Large Scale Matrix Optimization
Defeng Sun
 Vector TransportFree SVRG with General Retraction for Riemannian Optimization: Complexity Analysis and Practical Implementation
Bo Jiang
 On conjugate partialsymmetric complex tensors
Bo Jiang

Low Rank Matrix Approximations with HPC Applications (8 talks)
Hatem Ltaief, David Keyes
Lowrank matrix approximations have demonstrated attractive theoretical bounds, both in memory footprint and arithmetic complexity. In fact, they have even become numerical methods of choice when designing high performance applications, especially when looking at the forthcoming exascale era, where systems with billions of threads will be routine resources at hand. This minisymposium aims at bringing together experts from the field to assess the software adaptation of lowrank matrix computations into HPC applications.
 Fast LowRank Solvers for HPC Applications on Massively Parallel Systems
Hatem Ltaief
 GOFMM: A geometryoblivious fast multipole method for approximating arbitrary SPD matrices
George Biros
 A Parallel Implementation of a High Order Accurate Variable Coefficient Helmholtz Solver
Natalie Beams
 LowRank Matrix Approximations for Oil and Gas HPC Applications
Issam Said
 STARSH: a Hierarchical Matrix Market within an HPC Framework
Alexandr Mikhalev
 Matrixfree construction of HSS representations usingadaptive randomized sampling
Sherry Li
 Low Rank Approximations of Hessians for PDE Constrained Optimization
George Turkiyyah
 Simulations for the European Extremely Large Telescope using LowRank Matrix Approximations
Damien Gratadour

LowRank and ToeplitzRelated Structures in Applications and Algorithms (8 talks)
Stefano SerraCapizzano, Eugene Tyrtyshnikov
The minisymposium is focused on Structured Matrix Analysis, with the special target of shedding light on LowRank and Toeplitzrelated Structures. On sufficiently regular domains, certain combinations of such matrix objects weighted with proper diagonal sampling matrices are sufficient for describing in a great generality approximation of integrodifferential operators with variable coefficient, by means of (virtually) any type of discretization technique (finite elements, finite differences, isogeometric analysis, finite volumes etc). The considered topics and the young age of the speakers are aimed at fostering the contacts between PhD students, postdocs and young researchers, with a balanced choice of talks addressing at improving collaborations between analysis and applied research,showing connections among different methodologies,using the applications as a challenge for the search of more advanced algorithms.
 Multilinear and Linear Structures in Theory and Algorithms
Eugene Tyrtyshnikov
 Generalized Locally Toeplitz Sequences: a Link between Measurable Functions and Spectral Symbols
Giovanni Barbarino
 On the study of spectral properties of matrix sequences
Stanislav Morozov
 Cross method accuracy estimates in consistent norms
Alexander Osinsky
 Spectral and convergence analysis of the discrete Adaptive Local Iterative Filtering method by means of Generalized Locally Toeplitz sequences
Antonio Cicone
 Asymptotic expansion and extrapolation methods for the fast computation of the spectrum of large structured matrices
SvenErik Ekstrom
 Isogeometric analysis for 2D and 3D curldiv problems: Spectral symbols and fast iterative solvers
Hendrik Speleers
 Rissanenlike algorithm for block Hankel matrices in linear storage
Ivan Timokhin

Machine Learning: theory and practice (4 talks)
Haixia Liu, Yuan Yao
Summary: Machine learning is experiencing a period of rising impact on many areas of the sciences and engineering such as imaging, advertising, genetics, robotics, and speech recognition. On the other hand, it has deep roots in various aspects in mathematics, from optimization, approximation theory, to statistics, etc. This minisymposium aims to bring together researchers in different aspects of machine learning for discussions on the stateoftheart developments in theory and practice. The minisymposium has a total of four talks, which are about fast algorithms solving linear inequalities, genetic data analysis, theory and practice of deep learning.
 Approximation of inconsistent systems of linear inequalities: fast solvers and applications
Mila Nikolova
 Theory of Distributed Learning
DingXuan Zhou
 Scattering Transform for the Analysis and Classification of Art Images
Roberto Leonarduzzi
 TBA
Can Yang

Matrix Functions and their Applications (8 talks)
Andreas Frommer, Kathryn Lund, Massimiliano Fasi
Matrix functions are an important tool in many areas of scientific computing. They arise in the solution of differential equations, as the exponential, sine, or cosine; in graph and network analysis, as measurements of communicability and betweenness; and in lattice quantum chromodynamics, as the sign of the Dirac overlap operator. They also have many applications in statistics, theoretical physics, control theory, and machine learning.
Methods for computing matrix functions times a vector encompass a variety of numerical linear algebra tools, such as Gauss quadrature, Krylov subspaces, rational and polynomial approximations, and singular value decompositions.
Furthermore, many numerical analysis tools are used for analyzing the convergence and stability of these methods, as well as the condition number of $f(A)$ and decay bounds of its entries.
Given the rapid expansion of the literature on matrix functions in the last few years, this seminar fills an ongoing need to present and discuss stateoftheart techniques pertaining to matrix functions, their analysis, and applications.
 A harmonic Arnoldi method for computing the matrix function $f(A)v$
Zhongxiao Jia
 Superlinear convergence for matrix functions times a vector
Bernhard Beckermann
 A new framework for understanding block Krylov methods applied to matrix functions
Kathryn Lund
 Bounds for the decay of the entries in inverses and CauchyStieltjes functions of certain sparse normal matrices
Claudia Schimmel
 Matrix Means for Signed and Multilayer Graphs Clustering
Pedro Mercado Lopez
 A DaleckiiKrein formula for the Fr{é}chet derivative of SVDbased matrix functions
Vanni Noferini
 Computing matrix functions in arbitrary precision
Massimiliano Fasi
 Matrix function approximation for computational Bayesian statistics
Markus Hegland

Matrix Optimization and Applications (12 talks)
Xin Liu, Ting Kei Pong
In this session, we focus on optimization problems with matrix variables, including semidefinite programming problems, low rank matrix completion / decomposition problems, and orthogonal constrained optimization problems, etc. These problems arise in various applications such as bioinformatics, data analysis, image processing and materials science, and are also abundant in combinatorial optimization.
 Faster Riemannian Optimization using Randomized Preconditioning
Haim Avron
 Proximal gradient method and nonsmooth convex regression with cardinality penalty
Wei Bian
 Implementation of an ADMMtype firstorder method for convex composite conic programming
Liang Chen
 Relationship between three sparse optimization problems for multivariate regression
Xiaojun Chen
 Euclidean distance embedding for collaborative position localization with NLOS mitigation
Chao Ding
 An exact penalty method for semidefinitebox constrained lowrank matrix optimization problems
Tianxiang Liu
 A parallelizable algorithm for orthogonally constrained optimization problems
Xin Liu
 A nonmonotone alternating updating method for a class of matrix factorization problems
Ting Kei Pong
 Quadratic Optimization with Orthogonality Constraint: Explicit Lojasiewicz Exponent and Linear Convergence of RetractionBased LineSearch and Stochastic VarianceReduced Gradient Methods
Anthony ManCho So
 Algebraic properties for eigenvalue optimization
Yangfeng Su
 Local Geometry of Matrix Completion
Ruoyu Sun
 Quantum correlations: Conic formulations and matrix factorizations
Antonios Varvitsiotis

Nonlinear Eigenvalue Problems and Applications (8 talks)
Meiyue Shao, Roel Van Beeumen
Eigenvalue problems arise in many fields of science and engineering and their mathematical properties and numerical solution methods for standard, linear eigenvalue problems are well understood. Recent advances in several application areas resulted in a new type of eigenvalue problemthe nonlinear eigenvalue problem, $A(lambda)x=0$which exhibits nonlinearity in the eigenvalue parameter. Moreover, the nonlinear eigenvalue problem received more and more attention from the numerical linear algebra community during the last decade. So far, the majority of the work has been focused on polynomial eigenvalue problems.
In this minisymposium we will address the general nonlinear eigenvalue problem involving nonlinear functions such as exponential, rational, and irrational ones. Recent literature on numerical methods for solving these general nonlinear eigenvalue problems can, roughly speaking, be subdivided into three main classes: Newtonbased techniques, Krylov subspace methods applied to linearizations, and contour integration and rational filtering methods. Within this minisymposium we would like to address all three classes used to solve largescale nonlinear eigenvalue problems in different application areas.
 Handling square roots in nonlinear eigenvalue problems
Roel Van Beeumen
 Solving nonlinear eigenvalue problems using contour integration
Marc Van Barel
 Automatic rational approximation and linearization for nonlinear eigenvalue problems
Karl Meerbergen
 Robust Rayleigh quotient optimization and nonlinear eigenvalue problems
Ding Lu
 Conquering algebraic nonlinearity in nonlinear eigenvalue problems
Meiyue Shao
 Solving different rational eigenvalue problems via different types of linearizations
Froilán M. Dopico
 NEPPACK A Julia package for nonlinear eigenvalue problems
Emil Ringh
 A Pade Approximate Linearization for solving nonlinear eigenvalue problems in accelerator cavity design
Zhaojun Bai

Nonlinear PerronFrobenius theory and applications (4 talks)
Antoine Gautier, Francesco Tudisco
Nonlinear PerronFrobenius theory addresses problems such as existence, uniqueness and maximality of positive eigenpairs of different types of nonlinear and orderpreserving mappings.In recent years tools from this theory have been successfully exploited to address problems arising from a range of diverse applications and various areas, such as graph and hypergraph analysis, machine learning, signal processing, optimization and spectral problems for nonnegative tensors. This minisymposium sample some recent contributions in this field, covering advances in both the theory and the applications of PerronFrobenius theory for nonlinear mappings.
 Nonlinear PerronFrobenius theorem and applications to nonconvex global optimization
Antoine Gautier
 Node and Layer Eigenvector Centralities for Multiplex Networks
Francesca Arrigo
 Inequalities for the spectral radius and spectral norm of nonnegative tensors
Shmuel Friedland
 Some results on the spectral theory of hypergraphs
Jiang Zhou

Numerical Linear Algebra Algorithms and Applications in Data Science (7 talks)
Shuqin Zhang, Limin Li
Summary: Data science is currently one of the hottest research fields in many real applications such as medicine, business, finance, transportation, etc.. Lots of computational problems arise in the process of data modelling and data analysis. Due to the finite dimension property of the data samples, most computational problems can be transformed to linear algebra related problems. To date, numerical linear algebra has played important roles in data science.
With the fast development of experimental techniques and growth of internet communications, more and more data are generated nowdays. The availability of a huge amount of data brings big challenges for traditional computational methods. On one hand, to handle the big data matrices (high dimension, big sample size), algorithms having high computational speed and accuracy are in great need. This proposes the problem of improving the traditional methods such as SVD methods, conjugate gradient method, matrix preconditioning methods, and so on. On the other hand, with the generation of more data, many new models are proposed. This brings the chances for developing novel algorithms. Taking into account the properties of data to build good models and propose fast and accurate algorithms will accelerate the development of data science greatly. Numerical linear algebra as the essential technique for numerical algorithm development should be paid more attention.
The speakers in this minisymposium will discuss work that arises in data modelling including multiview data learning, data dimension reduction, data approximation, and stochastic data analysis. The numerical linear algebra methods cover lowdimension projection, matrix splitting, parallel SVD, conjugate gradient method, matrix preconditioning and so on. This minisymposium brings together researchers from different data analysis fields focusing on numerical linear algebra related algorithm development. It will emphasize the importance and strengthen the role of linear algebra in data science, thereby advances the collaborations for researchers from different fields.
 Simultaneous clustering of multiview data
Shuqin Zhang
 Uniform Projection for Multiview Learning
Limin Li
 Averaged information splitting for heterogeneously highthroughput data analysis
Shengxin Zhu
 A distributed parallel SVD algorithm based on the polar decomposition via Zolotarev's function
Shengguo Li
 A modified seasonal grey system model with fractional order accumulation for forecasting traffic flow
Yang Cao
 A Riemannian variant of FletcherReeves conjugate gradient method for stochastic inverse eigenvalue problems with partial eigendata
ZhengJian Bai
 A splitting preconditioner for implicit RungeKutta discretizations of a differentialalgebraic equation
Shuxin Miao

Numerical Methods for Ground and Excited State Electronic Structure Calculations (8 talks)
Anil Damle, Lin Lin, Chao Yang
Electronic structure theory and first principle calculations are among the most challenging and computationally demanding science and engineering problems. At their core, many of the methods used require the development of efficient and specialized linear algebraic techniques. This minisymposium aims to discuss new developments in the linear algebraic tools, numerical methods, and mathematical analysis used to achieve high levels of accuracy and efficiency in electronic structure theory. We bring together experts on electronic structure theory representing a broad set of computational approaches used in the field.
 A unified approach to Wannier interpolation
Anil Damle
 Potentialities of wavelet formalism towards a reduction of the complexity of large scale electronic structure calculations
Luigi Genovese
 Convergence analysis for the EDIIS algorithm
Tim Kelley
 A Semismooth Newton Method For Solving semidefinite programs inelectronic structure calculations
Zaiwen Wen
 Adaptive compression for HartreeFocklike equations
Michael Lindsey
 Latest developments of the polarizable continuum model within a domaindecomposition paradigm
Paolo Gatto
 Projected Commutator DIIS method for linear and nonlinear eigenvalue problems
Lin Lin
 Parallel transport evolution of timedependent density functional theory
Dong An

Optimization Methods on Matrix and Tensor Manifolds (8 talks)
Gennadij Heidel, Wen Huang
Riemannian optimization methods are a natural extension of Euclidean optimization methods: the search space is generalized from a Euclidean space to a manifold endowed with a Riemannian structure. This allows for many constrained Euclidean optimization problems to be formulated as unconstrained problems on Riemannian manifolds; the geometric structure can be exploited to provide mathematically elegant and computationally efficient solution methods by using tangent spaces as local linearizations.
Many important structures from linear algebra admit a Riemannian manifold structure, such as matrices with mutually orthogonal columns (Stiefel manifold), subspaces of fixed dimension (Grassmann manifold), positive definite matrices, or matrices of fixed rank.
The first session of this minisymposium will present some applications of the Riemannian optimization framework, such as blind deconvolution, computation of the Karcher mean, and lowrank matrix learning. It will also present novel results on subspace methods in Riemannian optimization.
The second session will be centered on the particular class of lowrank tensor manifolds, which make computations with multiway arrays of large dimension feasible and have attracted particular interest in recent research. It will present novel results on secondorder methods on tensor manifolds, such as trustregion or quasiNewton methods. It will also present results on dynamical approximation of tensor differential equations.
 Blind deconvolution by Optimizing over a Quotient Manifold
Wen Huang
 Riemannian optimization and the computation of the divergences and the Karcher mean of symmetric positive definite matrices
Kyle A. Gallivan
 A manifold approach to structured lowrank matrix learning
Bamdev Mishra
 Subspace methods in Riemannian manifold optimization
Weihong Yang
 QuasiNewton optimization methods on lowrank tensor manifolds
Gennadij Heidel
 Robust second order optimization methods on low rank matrix and tensor varieties
Valentin Khrulkov
 A Riemannian trust region method for the canonical tensor rank approximation problem
Nick Vannieuwenhoven
 Dynamical lowrank approximation of tensor differential equations
Hanna Walach

Parallel Sparse Triangular Solve on Emerging Platforms (4 talks)
Weifeng Liu, Wei Xue
Summary: Sparse triangular solve (SpTRSV) is an important building block in a number of numerical linear algebra routines such as sparse direct solvers and preconditioned sparse iterative solvers. Compared to dense triangular solve and other sparse basic linear algebra subprograms, SpTRSV is more difficult to parallelize since it is inherently sequential. The setbased methods (i.e., levelset and colorset) brought parallelism but also demonstrated high costs for preprocessing and runtime synchronization. In this proposed minisymposium, we will discuss current challenges and novel algorithms for SpTRSV on shared memory processors with homogeneous architectures (such as GPU and Xeon Phi) and with heterogeneous architectures (such as Sunway and APU), and distributed memory clusters. The objective of this minisymposium is to explore and discuss how emerging parallel platforms can help nextgeneration SpTRSV algorithm design.
 Scalability Analysis of Sparse Triangular Solve
Weifeng Liu
 Parallel Sparse Triangular Solve on Modern Manycore Processors: SynchronizationFree and 2D Blocking
Ang Li
 Refactoring Sparse Triangular Solve on Sunway TaihuLight Manycore Supercomputer
Wei Xue
 Enhancing Scalability of Parallel Sparse Triangular Solve in SuperLU
Yang Liu

Polynomial and Rational Matrices (8 talks)
Javier Pérez, Andrii Dmytryshyn
Polynomial and rational matrices have attracted much attention in the last years. Their appearance in numerous modern applications requires revising and improving known as well as developing new theories and algorithms concerning the associated eigenvalue problems, error and perturbation analyses, efficient numerical implementations, etc. This MiniSymposium aims to give an overview of the recent research on these topics, focusing on numerical stability of quadratic eigenvalue problem; canonical forms, that reveal transparently the complete eigenstructures; sensitivity of complete eigenstructures to perturbations; lowrank matrix pencils and matrix polinomials; blocktridiagonal linearizations; and structured eigenproblems associated with portHamiltonian systems.
 Stratifying complete eigenstructures: From matrix pencils to polynomials and back
Bo Kågström
 Blocksymmetric linearizations of odd degree matrix polynomials with optimal condition number and backward error
Maria Isabel Bueno
 Transparent Realizations for Polynomial and Rational Matrices
Steve Mackey
 Generic eigenstructures of matrix polynomials with bounded rank and degree
Andrii Dmytryshyn
 A backward stable quadratic eigenvalue solver
Françoise Tisseur
 A geometric description of the sets of palindromic and alternating matrix pencils with bounded ran
Fernando De Terán
 Second and higher order portHamiltonian systems and their first order representations
Volker Mehrmann
 On the stability of the twolevel orthogonal Arnoldi method for quadratic eigenvalue problems
Javier Pérez

Preconditioners for fractional partial differentialequations and applications (4 talks)
Daniele Bertaccini
Summary: Fractional partial differential equations (FDEs) are a strongly emerging tool every day more present in models in many applicative fields where, e.g.,nonlocal dynamics and anomalous diffusion are present such as in viscoelastic and polymeric materials, in control theory, economy, etc.
In this minisymposium proposal we plan to give a short but quite illustrative overview of the potentialities and of the related convergence theory for some ahhoc innovative preconditioning techniques for the iterative solution of the large (but full!) linear systems generated by the discretization of the underlying FDE models. The numerical solution of the underlying linear systems isan important research area as such equations pose substantial challenges to existing algorithms.
 Limited memory block preconditioners for fast solution of timedependent fractional PDEs
Fabio Durastante
 Spectral analysis and multigrid preconditioners for spacefractional diffusion equations
Maria Rosa Mazza
 Fast tensor solvers for optimization problems with FDEconstraints
Martin Stoll
 Preconditioner for Fractional Diffusion Equations with Piecewise Continuous Coefficients
Haiwei Sun

Preconditioners for illconditioned linear systems in large scale scientific computing (8 talks)
Luca Bergamaschi, Massimiliano Ferronato, Carlo Janna
Summary: The efficient solution to sparse linear systems is quite a common issue in several real world applications and often represents the main memoryand timeconsuming task in a computer simulation. In many areas of large scale engineering and scientific computing, the solution to large, sparse and very illconditioned systems relies on iterative methods which need appropriate preconditioning to achieve convergence in a reasonable number of iterations. The aim of this minisymposium is to present stateoftheart scalar and parallel preconditioning techniques with particular focus on
1. block preconditioners for indefinite systems
2. multilevel preconditioners
3. preconditionersfor leastsquares problems
4. lowrank updates of preconditioners
 Robust AMG interpolation with target vectors for elasticity problems
Ruipeng Li
 A Multilevel Preconditioner for Data Assimilation with 4DVar
Alison Ramage
 Algebraic Multigrid: Theory and Practice
James Joseph Brannick
 Preconditioning for multiphysics problems: A general framework
Massimiliano Ferronato
 Preconditioners for inexactNewton methods based on compactrepresentation of Broyden class updates
J.~Marín
 Preconditioning for TimeDependent PDEConstrained Optimization
John Pearson
 Multigrid preconditioning techniques for geophysical electromagnetics
Hisham bin Zubair Syed
 Spectral preconditioners for sequences of illconditioned linear systems
Luca Bergamaschi

Preconditioning for PDE Constrained Optimization (4 talks)
Roland Herzog, John Pearson
The field of PDEconstrained optimization provides a gateway to the study of many realworld processes from science and industry.As these problems typically lead to hugescale matrix systems upon discretization, it is therefore crucial to develop fast and efficient numerical solvers tailored specifically to the application at hand.Significant progress has been made in recent years, and research is now shifting to more challenging problems, e.g., obtaining parameter robust iterations and solving coupled multiphysics systems.In this minisymposium we wish to draw upon stateoftheart preconditioners to accelerate the convergence of iterative methods when applied to such problems.Speakers in this session will also provide an outlook to future challenges in the field.
 Preconditioners for PDE constrained optimization problems with coarse distributed observations
KentAndre Mardal
 Preconditioning for multiple saddle point problems
Walter Zulehner
 New Poissonlike preconditioners for fast and memoryefficient PDEconstrained optimization
Lasse Hjuler Christiansen
 Preconditioning for TimeDependent PDEs and PDE Control
Andrew Wathen

Randomized algorithms for factorizing matrices (4 talks)
PerGunnar Martinsson
Summary: Methods based on randomized projections have over the last several years proven to provide powerful tools for computing lowrank approximations to matrices. This minisymposium will explore recent research that demonstrates that the underlying ideas can also be used to solve other linear algebraic problems of high importance in applications. Problems addressed include how to compute extit{full} factorizations of matrices, how to compute matrix factorizations where the factors are required to have nonnegative entries, how to compute matrix factorizations under constraints on how matrix entries can be accessed, solving linear systems, and more. The common theme is a focus on high practical efficiency.
 Randomized Nonnegative Matrix Factorizations
Benjamin Erichson
 A randomized blocked algorithm for computing a rankrevealing UTV matrix decomposition
Nathan Heavner
 Randomized algorithms for imaging applications
Sergey Voronin
 Stabilized streaming algorithms for computing approximate matrix factorizations via randomized projections
Abinand Gopal

Rank structured methods for challenging numerical computations (8 talks)
Sabine Le Borne, Jianlin Xia
Summary: Rankstructured methods have demonstrated significant advantages in improving the efficiency and reliability of some largescale computations and engineering simulations. These methods extend the fundamental ideas of multipole and panelclustering methods to general nonlocal solution operators. While there exist various more or less closely related methods, the unifying aim of these methods is to explore efficient structured lowrank approximations, especially those exhibiting hierarchical or nested forms. These help the methods to achieve nearly linear complexity.
In this minisymposium, we aim to present and exchange recent new developments on rank structured methods for some challenging numerical problems such as high frequencies, ill conditioning, eigenvalue perturbation, and stability. Studies of structures, algorithm design, and accuracy control will be discussed. The minisymposium will include experts working on a broad range of rank structured methods.
 Hmatrices for stable computations in RBF interpolation problems
Sabine Le Borne
 How good are HMatrices at high frequencies?
Timo Betcke
 Local lowrank approximation for the highfrequency Helmholtz equation
Steffen Boerm
 Efficiency and Accuracy of Parallel Accumulatorbased HArithmetic
Ronald Kriemann
 Randomized techniques for fast eigenvalue solution
Jianlin Xia
 The perfect shift and the fast computation of roots of polynomials
Nicola Mastronardi
 Structured matrices in polynomial system solving
Simon Telen
 Preserving positive definiteness in HSS approximation and its application in preconditioning
Xin Xing

Rational Krylov Methods and Applications (8 talks)
Stefan Güttel, Patrick Kürschner
Rational Krylov methods have become an indispensable tool of scientific computing. Invented by Axel Ruhe for the solution of large sparse eigenvalue problems, these methods have seen an increasing number of other applications over the last two decades or so. Applications of rational Krylov methods are connected with model order reduction, matrix function approximation, matrix equations, nonlinear eigenvalue problems, and nonlinear rational least squares fitting, to name a few. This minisymposium aims to bring together experts to discuss recent progress on theoretical and numerical aspects of these methods as well as novel applications.
 The block rational Arnoldi algorithm
Steven Elsworth
 Rational Krylov Subspaces for Wavefield Applications
Jörn Zimmerling
 Krylov methods for Hermitian nonlinear eigenvalue problems
Giampaolo Mele
 Compressing variablecoefficient Helmholtz problems via RKFIT
Stefan Güttel
 Rational Krylov methods in discrete inverse problems
Volker Grimm
 Inexact Rational Krylov methods applied to Lyapunov equations
Melina Freitag
 Numerical methods for Lyapunov matrix equations with banded symmetric data
Davide Palitta
 A comparison of rational Krylov and related lowrank methods for large Riccati equations
Patrick Kürschner

Recent advances in linear algebra for uncertainty quantification (7 talks)
Zhiwen Zhang, Bin Zheng
The aim of this minisymposium is to present recent development of advanced linear algebra techniques for uncertainty quantification including, but are not limited to, preconditioning techniques and multigrid methods for stochastic partial differential equations, multifidelity methods in uncertainty quantification, hierarchical matrices and lowrank tensor approximations, compressive sensing and sparse approximations, model reduction methods for PDEs with stochastic and/or multiscale features, random matrix models, etc.
 Asymptotic analysis and numerical method for singularly perturbed eigenvalue problems
Zhongyi Huang
 An Adaptive Reduced Basis ANOVA Method for HighDimensional Bayesian Inverse Problems
Qifeng Liao
 Title: Randomized Kaczmarz method for linear inverse problems
Xiliang Lu
 TBA
Ju Ming
 Sequential data assimilation with multiple nonlinear models and applications to subsurface flow
Peng Wang
 A new model reduction technique for convectiondominated PDEs with random velocity fields
Guannan Zhang
 Gamblet based multilevel decomposition/preconditioner for stochastic multiscale PDE
Lei Zhang

Recent Advances in Tensor Based Data Processing (Part I) (4 talks)
Chuan Chen, Yi Chang, Yao Wang, XiLe Zhao
Summary: As a natural representation for highdimensional data (e.g., hyperspectral images and heterogeneous information network), tensor (i.e. multidimensional array) has recently becomeubiquitous in data analytics at the confluence ofstatistics, image processing and machine learning. The related advances in applied mathematics motivate us to gradually move from classical matrix based methods to tensor based methods for data processing problems, which could offer new tools to exploit the intrinsic multilinear structure. In this interdisciplinary research field, there are fast emerging works on tensor based theory, models, numerical algorithms, and applications on data processing. This minisymposium aims at promoting discussions among researchers investigating innovative tensor based approaches to data processing problems in both theoretical and practical aspects.
 Block Term Decomposition for Multilayer Networks Clustering
ZiTai Chen
 Hyperspectral Image Restoration via Tensorbased Priors: From Lowrank to Deep Model
Yi Chang
 Compressive Tensor Principal Component Pursuit
Yao Wang
 Lowrank tensor completion using parallelmatrix factorization with factor priors
XiLe Zhao

Recent Advances in Tensor Based Data Processing (Part II) (4 talks)
Chuan Chen, Yi Chang, Yao Wang, XiLe Zhao
Summary: As a natural representation for highdimensional data (e.g., hyperspectral images and heterogeneous information network), tensor (i.e. multidimensional array) has recently becomeubiquitous in data analytics at the confluence ofstatistics, image processing and machine learning. The related advances in applied mathematics motivate us to gradually move from classical matrix based methods to tensor based methods for data processing problems, which could offer new tools to exploit the intrinsic multilinear structure. In this interdisciplinary research field, there are fast emerging works on tensor based theory, models, numerical algorithms, and applications on data processing. This minisymposium aims at promoting discussions among researchers investigating innovative tensor based approaches to data processing problems in both theoretical and practical aspects.
 Data Mining with Tensor based Methods
XuTao Li
 Lowrank Tensor Analysis with Noise Modeling
Zhi Han
 Hyperspectral and Multispectral Image Fusion Via Total Variation Regularized Nonlocal Tensor Train Decomposition
KaiDong Wang
 A Novel Tensorbased Video Rain Streaks Removal Approach via UtilizingDiscriminatively Intrinsic Priors
LiangJian Deng

Recent applications of rank structures in matrix analysis (8 talks)
Thomas Mach, Stefano Massei, Leonardo Robol
The development of applied science and engineering raised attention on large scale problems, generating an increasing demand of computational effort. In many practical situations, the only way to satisfy this request is to exploit obvious and hidden structures in the data. In this context, rank structures constitute a powerful tool for reaching this goal.
Many realworld problems are analyzed by means of algebraic techniques that exploit lowrank structures: fast multipole methods, discretization of PDEs and integral equations, efficient solution of matrix equations, and computation of matrix functions.
The representation and the theoretical analysis of these algebraic objects is of fundamental importance to devise fast algorithms. Several representations have been proposed in the literature: $\mathcal{H}$, $\mathcal{H}^{2}$, and HSS matrices, quasiseparable and semiseparable structures. The design of fast methods relying on these representations is currently an active branch of numerical linear algebra. The talks in this minisymposium present some recent advances in this field.
 Low rank updates and a divide and conquer method for matrix equations
Stefano Massei
 $RQZ$: A rational $QZ$ algorithm for the generalized eigenvalue problem
Daan Camps
 Fast direct algorithms for least squares and least norm solutions for hierarchical matrices
Abhay Gupta
 Computing the inverse matrix $phi_1$function for a quasiseparable matrix
Luca Gemignani
 Superfast direct solvers for 3D MSN PDE solvers
Shiv Chandrasekaran
 Fast direct solvers for boundary value problems on globally evolving geometries
Adrianna Gillman
 Matrix Aspects of Fast Multipole Method
Xiaofeng Ou
 Adaptive Cross Approximation for IllPosed Problems
Thomas Mach

Some recent applications of Krylov subspace methods (10 talks)
Yunfeng Cai, LeiHong Zhang
Summary: Krylov subspace methods are generally accepted as one of the most efficient methodsfor solving large sparse linear system of equations and eigenvalue problems. Traditionally, many famous Krylov subspace methods such as PCG, MINRES, GMRES, etc. for linear system of equations, and Lanczos and Arnoldi methods (also their variants) for eigenvalue problems, have been developed, and have been successfully solving numerous crucially important problems in science and engineering. One of recent trends of the Krylov subspace method is to extend its power to solve other important realworld applications. Along this line, we propose this minisymposium by carefully choosing the following talks on some recent/new applications of Krylov subspace methods. These talks cover the applications of Krylov methods on optimization, tensor analysis, data mining, linear systems, eigenvalue problems, and preconditioning.Through this minisymposium, we hope to reveal the power of Krylov subspace methods in solving these applications, and stimulate other more important developments.
 Preconditioning for Accurate Solutions of Linear Systems and Eigenvalue Problems
Qiang Ye
 A block term decomposition of high order tensors
Yunfeng Cai
 A Fast Implementation On The Exponential Marginal Fisher Analysis For High Dimensionality Reduction
Gang Wu
 Deflated block Krylov subspace methods for large scale eigenvalue problems
Qiang Niu
 Lanczos type methods for the linear response eigenvalue problem
Zhongming Teng
 Sparse frequent direction algorithm for low rank approximation
Delin Chu
 On the Generalized Lanczos TrustRegion Method
LeiHong Zhang
 A Block Lanczos Method for the Extended TrustRegion Subproblems
Weihong Yang
 Parametrized quasisoft thresholding operator for compressed sensing and matrix completion
AnBao Xu
 Twolevel RAS preconditioners of Krylov subspace methods for large sparse linear systems
Xin Lu

Tensor Analysis, Computation, and Applications I (8 talks)
Weiyang Ding
Summary: The term {it tensor} has both meanings of a geometric object and a multiway array. Applications of tensors include various disciplines in science and engineering, such as mechanics, quantum information, signal and image processing, optimization, numerical PDE, and hypergraph theory. There are several hot research topics on tensors, such as tensor decomposition and lowrank approximation, tensor spectral theory, tensor completion, tensorrelated systems of equations, and tensor complementarity problems. Researchers in all these mentioned areas will give presentations to broaden our perspective on tensor research. This is one of a series minisymposia and focuses more on applications of tensors and structured tensors.
 Applications of tensor eigenvalues in physics
Liqun Qi
 The rank of $Wotimes W$ is eight
Shmuel Friedland
 Optimization methods using matrix and tensor structures
Eugene Tyrtyshnikov
 Exploitation of structure in largescale tensor decompositions
Lieven De Lathauwer
 An Adaptive Correction Approach for Tensor Completion
Minru Bai
 Generalized polynomial complementarity problems with structured tensors
Chen Ling
 Copositive Tensor Detection and Its Applications in Physics and Hypergraphs
Haibin Chen
 The bound of Heigenvalue of some structure tensors with entries in an interval
Lubin Cui

Tensor Analysis, Computation, and Applications II (8 talks)
Shenglong Hu
Summary: The term {it tensor} has both meanings of a geometric object and a multiway array. Applications of tensors include various disciplines in science and engineering, such as mechanics, quantum information, signal and image processing, optimization, numerical PDE, and hypergraph theory. There are several hot research topics on tensors, such as tensor decomposition and lowrank approximation, tensor spectral theory, tensor completion, tensorrelated systems of equations, and tensor complementarity problems. Researchers in all these mentioned areas will give presentations to broaden our perspective on tensor research. This is one of a series minisymposia and focuses more on tensor analysis and algorithm design.
 The Fiedler vector of a Laplacian tensor for hypergraph partitioning
Yannan Chen
 Solving tensor problems via continuation methods
Lixing Han
 Local convergence rate analysis for the higherorder power method in best rank one approximations of tensors
Guoyin Li
 Tensor splitting methods for solving the multilinear system
Wen Li
 Sparse Tucker decomposition completion for 3D facial expression recognition
Ziyan Luo
 Tensor ranks and secant varieties
Yang Qi
 Slemma of the fourth order tensor systems
Qingzhi Yang
 Hankel Tensor Decompositions and Ranks
Ke Ye

TensorBased Modelling (4 talks)
Lieven De Lathauwer
Summary: An important trend is the extension of applied linear algebra to applied multilinear algebra. The developments gradually allow a transition from classical vector and matrix based methods to methods that involve tensors of arbitrary order. Tensor decompositions open up various new avenues beyond the realm of matrix methods. This minisymposium presents tensor decompositions as new modelling tools. A range of applications in signal processing, data analysis, system modelling en computing is discussed.
 Prewhitening under channeldependent signaltonoise ratios
Chuan Chen
 Tensor decompositions in reduced order models
Youngsoo Choi
 Block tensor train decomposition for singular value decomposition and missing data estimation
Namgil Lee
 Nonlinear system identification with tensor methods
Kim Batselier

Tensors and multilinear algebra (8 talks)
Anna Seigal, André Uschmajew, Bart Vandereycken
Tensors in the form of multidimensional arrays have seen an increasing interest in recent years in the context of modern data analysis and highdimensional equations in numerical analysis. Higherorder tensors are a natural generalization of matrices and, just as for matrices, their lowrank decompositions and spectral properties are important for applications. In the multilinear setting of tensors, however, analyzing such structures is challenging and requires conceptually new tools. Many techniques investigate and manipulate unfoldings (flattenings) of tensors into matrices, where linear algebra operations can be applied. In this respect, the subject of tensors and multilinear algebra fits a conference on applied linear algebra in two ways, as it occurs in many modern applications, and requires linear algebra for its treatment.
In this minisymposium, we wish to bring the latest developments in this area to attention, and promote it as an active and attractive research field to people interested in linear algebra. Contrary to the other sessions on tensors, this session will focus on algebraic foundations and spectral properties of tensors that are important in understanding their lowrank approximations.
 The condition number of the canonical polyadic tensor decomposition
Paul Breiding
 Geometrical description of feasible singular values in tree tensor formats
Sebastian Kraemer
 The positive cone to algebraic varieties of hierarchical tensors
Benjamin Kutschan
 Nuclear decomposition of higherorder tensors
LekHeng Lim
 Lowrank Riemannian optimization for highdimensional eigenvalue problems
Maksim Rakhuba
 Decomposing Tensors into Equiangular Tight Frames
Elina Robeva
 Duality of graphical models and tensor networks
Anna Seigal
 Orthogonal tensors and rankone approximation ratio
Andre Uschmajew

The Perturbation Theory and StructurePreserving Algorithms (8 talks)
ZhengJian Bai, Tiexiang Li, Hanyu Li, ZhiGang Jia
Summary: The perturbation theory provides reliability and stability analysis of scientific systems and algorithms, and has been one of the most important topics in numerical analysis. Recently, the perturbation theory has been involved in various fields, including the nonlinear eigenvalue/eigenvector problem, the generalized least square problem, the tensor analysis, the random methods for big data analysis, etc. For example, one crucial subject is to analyze the backward and forward errors of the eigenvectordependent eigenvalue problem from solving the discrete KohnSham equations.With a rigorous selection, we propose this minisymposium containing eight presentations on the recent development of the perturbation theory and related works.These presentations include the forward and backward errors of the nonlinear eigenvectors, the random perturbation intervals of symmetric eigenvalue problem, the statistical condition estimation, and the structurepreserving algorithms. The final aim of this minisymposium is to reveal the new tools in the perturbation theory, and put forward the research of the new methods and subjects in this important field.
 Perturbation Analysis of an Eigenvector Dependent Nonlinear Eigenvalue Problem with Applications
ZhiGang Jia
 Improved random perturbation intervals of symmetric eigenvalue problem
Hanyu Li
 Error Bounds for Approximate Deflating Subspaces of Linear Response Eigenvalue Problems
WeiGuo Wang
 Relative Perturbation Bounds for Eigenpairs of the Diagonalizable Matrices
Yanmei Chen
 Small Sample Statistical Condition Estimation for the Total Least Squares Problem
Huaian Diao
 Some perturbation results for Joint Block Diagonalization problems
Decai Shi
 A StructurePreserving ${Gamma}$Lanczos Algorithm for BetheSalpeter Eigenvalue Problems
Tiexiang Li
 A StructurePreserving Jacobi Algorithm for Quaternion Hermitian Eigenvalue Problems
RuRu Ma

The Spectrum of Hypergraphs via Tensors (8 talks)
Xiying Yuan
Summary:
Many graph problems have been successfully solved with linear methods by employing the associated matrices for graphs. As generalized from graphs, hypergraphs are now studied through their representations by tensors, an extended concept of matrices. This minisymposium mainly focuses on recent results related to the spectrum of uniform hypergraphs via tensors, some relevent algorithms and their possible applications in the study of hypernetworks.
 On the analytic connectivity of uniform hypergraphs
Changjiang Bu
 Some recent results on the tensor spectrum of hypergraphs
An Chang
 The spectral symmetry and stabilizing property of tensors and hypergraphs
Yizheng Fan
 Tensor and the spectral radius of uniform hypergraphs
Liying Kang
 Some results on spectrum of graphs
Mei Lu
 Spectral Radius of ${0, 1}$Tensor with Prescribed Number of Ones
Linyuan Lu
 Some results in spectral (hyper)graph theory
Xiaodong Zhang
 On distance Laplacian spectral radius of graphs
Bo Zhou

Tridiagonal matrices and their applications in physics and mathematics (8 talks)
Natalia Bebiano, Mikhail Tyaglov
Summary: Tridiagonal matrices emerge in plenty of applications in science and engineering. They are used for solving a variety of problems in disparate contexts. Beyond their several applications seldom discussed, the methods, techniques, and theoretical framework used in this research field make it very interesting and challenging.In this minisymposium we attract people from different areas of mathematics who use tridiagonal matrices in their study to discuss recent developments, new approaches and perspectives as well as new applications of tridiagonal matrices.
 On von Neumann and Rényi entropies of rings and paths
Natália Bebiano
 Tridiaglonal matrices with only one eigenvalue and their relations to polynomials orthogonal with nonHermitian weight
Mikhail Tyaglov
 Positivity and Recursion formula of the linearization coefficients of Bessel polynomials
M. J. Atia
 Ultradiscrete analogue of the qd algorithm for MinPlus tridiagonal matrix
Akiko Fukuda
 A generalized eigenvalue problem with two tridiagonal matrices
Alagacone Sri Ranga
 Eigenvalue problems of structured band matrices related to discrete integrable systems
Masato Shinjo
 On instability of the absolutely continuous spectrum of dissipative Schrödinger operators and Jacobi matrices
Roman Romanov
 Blocktridiagonal linearizations of matrix polynomials
Susana Furtado


