Accepted Minisymposia

 MS01 Advances in High-Performance Sparse Matrix Computation (4 talks) Mathias Jacquelin, Esmond Ng 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 large-scale scientific problems. Towards highly scalable asynchronous sparse solvers for symmetric matricesEsmond Ng Fine-grained Parallel Incomplete LU FactorizationEdmond Chow Approximate sparse matrix factorization using low-rank compressionPieter Ghysels Hiding latencies and avoid communications in Krylov solversCools Siegfried MS02 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. Conjugate gradient for nonsingular saddle-point systems with a highly singular leading blockMichael Wathen Symmetrizing nonsymmetric Toeplitz matrices in fractional diffusion problemsJennifer Pestana Commutator Based Preconditioning for Incompressible Two-Phase FlowNiall Bootland The efficient solution of linear algebra subproblems arising in optimization methodsTyrone Rees MS03 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 fixed-point 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 UpdatesMing Yan Asynchronous Domain Decomposition SolversChristian Glusa Asynchronous Linear System Solvers on SupercomputersTeodor Nikolov Asynchronous Optimized Schwarz Methods for Poisson's Equation in Rectangular DomainsJosé Garay MS04 Constrained Low-Rank Matrix and Tensor Approximations (8 talks) Grey Ballard, Ramakrishnan Kannan, Haesun Park Constrained low rank matrix and tensor approximations are extremely useful in large-scale 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 application-dependent constraints. Joint Nonnegative Matrix Factorization for Hybrid Clustering based on Content and Connection StructureHaesun Park Tensor decompositions for big multi-aspect data analyticsEvangelos Papalexakis Speeding Up Tensor Contractions through Extended BLAS KernelsYang Shi SUSTain: Scalable Unsupervised Scoring for Tensors and its Application to PhenotypingIoakeim Perros Accelerating the Tucker Decomposition with Compressed Sparse TensorsGeorge Karypis Efficient CP-ALS and Reconstruction from CP FormJed Duersch Non-negative Sparse Tensor Decomposition on Distributed SystemsJiajia Li Communication-Optimal Algorithms for CP Decompositions of Dense TensorsGrey Ballard MS05 Coupled matrix and tensor decompositions: Theory and methods (3 talks) Dana Lahat Matrices and higher-order arrays, also known as tensors, are natural structures for data representation, and their factorizations in low-rank 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 low-rank terms, as well as to coupled Sylvester-type matrix equations. We compare the gain that can be achieved from computing coupled CP decompositions of tensors in a semi-algebraic 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 low-rank block terms using Schur's lemma on irreducible representationsDana Lahat Decoupling multivariate polynomials: comparing different tensorization methodsPhilippe Dreesen Coupled and uncoupled sparse-Bayesian non-negative matrix factorization for integrated analyses in genomicsElana J. Fertig MS06 Discovery from Data (12 talks) Sri Priya Ponnapalli, Katherine A. Aiello, Orly Alter The number of large-scale high-dimensional 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 Copy-Number Alterations Revealed by the GSVD and Tensor GSVD Encode for Cell Transformation and Predict Survival and Response to Platinum in AdenocarcinomasOrly Alter Systems Biology of Drug Resistance in CancerAntti Hakkinen Single-Cell Entropy for Estimating Differentiation Potency in Waddington's Epigenetic LandscapeAndrew E. Teschendorff Dimension Reduction for the Integrative Analysis of Multilevel Omics DataGerhard G. Thallinger Mathematically Universal and Biologically Consistent Astrocytoma Genotype Encodes for Transformation and Predicts Survival PhenotypeSri Priya Ponnapalli Statistical Methods for Integrative Clustering Analysis of Multi-Omics DataQianxing Mo Structured Convex Optimization Method for Orthogonal Nonnegative Matrix Factorization with Applications to Gene Expression DataJunjun Pan Mining the ECG Using Low Rank Tensor Approximations with Applications in Cardiac MonitoringSabine Van Huffel Tensor Higher-Order GSVD: A Comparative Spectral Decomposition of Multiple Column-Matched but Row-Independent Large-Scale High-Dimensional DatasetsSri Priya Ponnapalli The GSVD: Where are the Ellipses?Alan Edelman Tensor convolutional neural networks (tCNN): Improved featurization using high-dimensional frameworksElizabeth Newman Three-way Generalized Canonical Correlation AnalysisArthur Tenenhaus MS07 Domain decomposition methods for heterogeneous and large-scale 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 mini-symposium, we will review some recent advances in the use of domain decomposition and related methodsto solve complex heterogeneous and large-scale problems. Fast solvers for multiscale problems: overlappingdomain decomposition methodsHyea Hyun Kim A parallel non-iterative domain decomposition method for image denoisingXiao-chuan Cai Robust BDDC and FETI-DP methods in PETScStefano Zampini Goal-oriented adaptivity for a class of multiscale high contrast flow problems Sai-Mang Pun A Parareal Algorithm for Coupled Systems Arising from Optimal Control ProblemsFelix Kwok Convergence of Adaptive Weak Galerkin Finite Element MethodsLiuqiang Zhong A nonoverlapping DD method for an interior penalty methodEun-Hee Park A two-grid preconditioner for flow simulations in highly heterogeneous media with an adaptive coarse spaceShubin Fu MS08 Efficient Kernel Methods and Numerical Linear Algebra (8 talks) Evgeny Burnaev, Ivan Oseledets Despite their theoretical appeal and grounding in tractable convex optimization techniques, kernel methods are often not the first choice for large-scale 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 scale-up 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 MethodsEvgeny Burnaev Kernel methods and tensor decompositionsIvan Oseledets Quadrature-based features for kernel approximationErmek Kapushev Convergence Analysis of Deterministic Kernel-based Quadrature Rules in Sobolev SpacesMotonobu Kanagawa Sequential Sampling for Kernel Matrix Approximation and Online LearningMichal Valko Tradeoffs of Stochastic Approximation in Hilbert SpacesAymeric Dieuleveut Scalable Deep Kernel LearningAndrew Gordon Wilson Kernel Methods for Causal InferenceKrikamol Muandet MS09 Exploiting Low-Complexity Structures in Data Analysis: Theory and Algorithms (7 talks) Ju Sun, Ke Wei Low-complexity structures are central to modern data analysis --- they are exploited to tame data dimensionality, to rescue ill-posed 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 low-rank 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 worst-case 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 low-complexity structures will be discussed, with an emphasis on addressing the new challenges. Geometry and Algorithm for Sparse Blind Deconvolution Yuqian Zhang The Scaling Limit of Online Lasso, Sparse PCA and Related AlgorithmsYue M. Lu Accelerated Alternating Projection for Robust Principle Component AnalysisJian-Feng Cai Numerical integrators for rank-constrained differential equationsBart Vandereycken Foundations of Nonconvex and Nonsmooth Robust Subspace RecoveryTyler Maunu On Mathematical Theories of Deep Learning Yuan Yao Convergence of the randomized Kaczmarz method for phase retrievalHalyun Jeong MS10 Generalized Inverses and the Linear Least Squares (8 talks) Dragana Cvetkovic Ilic, Ken Hayami, Yimin Wei 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 integer-valued signalsXiao-Wen Chang Computing time-varying ML-weighted pseudoinverse by the Zhang neural networksSanzheng Qiao GNN and ZNN solutions of linear matrix equationsPredrag S. Stanimirović Randomized Algorithms forTotal Least Squares ProblemsYimin Wei Randomized Algorithms for Core Problem and TLS problemLiping Zhang Condition Numbers of the Multidimensional Total Least Squares ProblemBing Zheng Fast solution of nonnegative matrix factorization via a matrix-based active set methodNing Zheng Computing the Inverse and Pseudoinverse of Time-Varying Matrices by the Discretization of Continuous-Time ZNN ModelsMarko D. Petković MS11 Iterative Solvers for Parallel-in-Time Integration (4 talks) Xiao-Chuan 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 time-stepping is a computational bottleneck when attempting to implement highly concurrent algorithms, thus parallel-in-time methods are desirable. This minisymposium will present recent advances in iterative solvers for parallel-in-time integration. This includes methods like parareal, multigrid reduction, and parallel space-time methods, with application to linear and nonlinear PDEs of parabolic and hyperbolic type. Space-Time Schwarz Preconditioning and ApplicationsXiao-Chuan Cai Parallel-in-Time Multigrid with Adaptive Spatial Coarsening for the Linear Advection and Inviscid Burgers EquationsHans De Sterck On the convergence of PFASSTMatthias Bolten Waveform Relaxation with Adaptive Pipelining (WRAP)Felix Kwok MS12 Large-scale eigenvalue problems and applications (10 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 large-scale 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. An O(N^3) Scaling Algorithm to Calculate O(N) Excited States Based on PP-RPAHaizhao Yang The ELSI Infrastructure for Large-Scale Electronic Structure TheoryVolker Blum Recent Progress on Solving Large-scale Eigenvalue Problems in Electronic Structure CalculationsChao Yang The Full Configuration Interaction Quantum Monte Carlo(FCIQMC) in the lens of inexact power iterationZhe Wang A FEAST Algorithm with oblique projection for generalized eigenvalue problemsGuojian Yin Real eigenvalues in linear viscoelastic oscillatorsHeinrich Voss Error bounds for Ritz vectors and approximate singular vectorsYuji Nakatsukasa Consistent symmetric greedy coordinate descent methodYingzhou Li On the accuracy of fast structured eigenvalue solutionsJimmy Vogel Generation of large sparse test matrices to aid the development of large-scale eigensolversPeter Tang MS13 Large-scale matrix and tensor optimization (4 talks) Yangyang Xu Matrix and tensor optimization problems naturally arise from applications that involve two-dimensional or multi-dimensional 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 large-scale matrix and tensor optimization. Greedy method for orthogonal tensor decompositionYangyang Xu SDPNAL+: A MATLAB software package for large-scale SDPs with a user-friendly interfaceDefeng Sun Vector Transport-Free SVRG with General Retraction for Riemannian Optimization: Complexity Analysis and Practical ImplementationBo Jiang On conjugate partial-symmetric complex tensorsBo Jiang MS14 Low Rank Matrix Approximations with HPC Applications (8 talks) Hatem Ltaief, David Keyes Low-rank 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 low-rank matrix computations into HPC applications. Fast Low-Rank Solvers for HPC Applications on Massively Parallel SystemsHatem Ltaief GOFMM: A geometry-oblivious fast multipole method for approximating arbitrary SPD matricesGeorge Biros A Parallel Implementation of a High Order Accurate Variable Coefficient Helmholtz SolverNatalie Beams Low-Rank Matrix Approximations for Oil and Gas HPC ApplicationsIssam Said STARS-H: a Hierarchical Matrix Market within an HPC FrameworkAlexandr Mikhalev Matrix-free construction of HSS representations usingadaptive randomized samplingSherry Li Low Rank Approximations of Hessians for PDE Constrained OptimizationGeorge Turkiyyah Simulations for the European Extremely Large Telescope using Low-Rank Matrix ApproximationsDamien Gratadour MS15 Low-Rank and Toeplitz-Related Structures in Applications and Algorithms (8 talks) Stefano Serra-Capizzano, Eugene Tyrtyshnikov The mini-symposium is focused on Structured Matrix Analysis, with the special target of shedding light on Low-Rank and Toeplitz-related 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 integro-differential 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 AlgorithmsEugene Tyrtyshnikov Generalized Locally Toeplitz Sequences: a Link between Measurable Functions and Spectral SymbolsGiovanni Barbarino On the study of spectral properties of matrix sequencesStanislav Morozov Cross method accuracy estimates in consistent normsAlexander Osinsky Spectral and convergence analysis of the discrete Adaptive Local Iterative Filtering method by means of Generalized Locally Toeplitz sequencesAntonio Cicone Asymptotic expansion and extrapolation methods for the fast computation of the spectrum of large structured matricesSven-Erik Ekstrom Isogeometric analysis for 2D and 3D curl-div problems: Spectral symbols and fast iterative solversHendrik Speleers Rissanen-like algorithm for block Hankel matrices in linear storageIvan Timokhin MS16 Machine Learning: theory and practice (4 talks) Haixia Liu, Yuan Yao 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 mini-symposium aims to bring together researchers in different aspects of machine learning for discussions on the state-of-the-art developments in theory and practice. The mini-symposium 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 applicationsMila Nikolova Theory of Distributed LearningDing-Xuan Zhou Scattering Transform for the Analysis and Classification of Art ImagesRoberto Leonarduzzi TBACan Yang MS17 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 state-of-the-art techniques pertaining to matrix functions, their analysis, and applications. A harmonic Arnoldi method for computing the matrix function $f(A)v$Zhongxiao Jia A new framework for understanding block Krylov methods applied to matrix functionsKathryn Lund Bounds for the decay of the entries in inverses and Cauchy-Stieltjes functions of certain sparse normal matricesClaudia Schimmel Matrix Means for Signed and Multi-layer Graphs ClusteringPedro Mercado Lopez A Daleckii--Krein formula for the Fréchet derivative of SVD-based matrix functionsVanni Noferini Computing matrix functions in arbitrary precisionMassimiliano Fasi Matrix function approximation for computational Bayesian statisticsMarkus Hegland Conditioning of the Matrix-Matrix ExponentiationJoão R. Cardoso MS18 Matrix Optimization and Applications (11 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 bio-informatics, data analysis, image processing and materials science, and are also abundant in combinatorial optimization. Faster Riemannian Optimization using Randomized PreconditioningHaim Avron Smoothing proximal gradient method for nonsmooth convex regression with cardinality penaltyWei Bian Implementation of an ADMM-type first-order method for convex composite conic programmingLiang Chen Relationship between three sparse optimization problems for multivariate regressionXiaojun Chen Euclidean distance embedding for collaborative position localization with NLOS mitigationChao Ding An exact penalty method for semidefinite-box constrained low-rank matrix optimization problemsTianxiang Liu A parallelizable algorithm for orthogonally constrained optimization problemsXin Liu A non-monotone alternating updating method for a class of matrix factorization problemsTing Kei Pong Quadratic Optimization with Orthogonality Constraint: Explicit Lojasiewicz Exponent and Linear Convergence of Retraction-Based Line-Search and Stochastic Variance-Reduced Gradient MethodsAnthony Man-Cho So Algebraic properties for eigenvalue optimizationYangfeng Su Local Geometry of Matrix CompletionRuoyu Sun MS19 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 problem---the 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: Newton-based 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 large-scale nonlinear eigenvalue problems in different application areas. Handling square roots in nonlinear eigenvalue problemsRoel Van Beeumen Solving nonlinear eigenvalue problems using contour integrationSimon Telen Automatic rational approximation and linearization for nonlinear eigenvalue problemsKarl Meerbergen Robust Rayleigh quotient optimization and nonlinear eigenvalue problemsDing Lu Conquering algebraic nonlinearity in nonlinear eigenvalue problemsMeiyue Shao Solving different rational eigenvalue problems via different types of linearizationsFroilán M. Dopico NEP-PACK A Julia package for nonlinear eigenvalue problemsEmil Ringh A Pade Approximate Linearization for solving nonlinear eigenvalue problems in accelerator cavity designZhaojun Bai MS20 Nonlinear Perron-Frobenius theory and applications (4 talks) Antoine Gautier, Francesco Tudisco Nonlinear Perron-Frobenius theory addresses problems such as existence, uniqueness and maximality of positive eigenpairs of different types of nonlinear and order-preserving 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 Perron-Frobenius theory for nonlinear mappings. Nonlinear Perron-Frobenius theorem and applications to nonconvex global optimizationAntoine Gautier Node and Layer Eigenvector Centralities for Multiplex NetworksFrancesca Arrigo Inequalities for the spectral radius and spectral norm of nonnegative tensorsShmuel Friedland Some results on the spectral theory of hypergraphsJiang Zhou MS21 Numerical Linear Algebra Algorithms and Applications in Data Science (6 talks) Shuqin Zhang, Limin Li 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 low-dimension 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 dataShuqin Zhang Averaged information splitting for heterogeneously high-throughput data analysisShengxin Zhu A modified seasonal grey system model with fractional order accumulation for forecasting traffic flowYang Cao A distributed parallel SVD algorithm based on the polar decomposition via Zolotarev's functionShengguo Li A Riemannian variant of Fletcher-Reeves conjugate gradient method for stochastic inverse eigenvalue problems with partial eigendataZheng-Jian Bai A splitting preconditioner for implicit Runge-Kutta discretizations of a differential-algebraic equationShuxin Miao MS22 Numerical Methods for Ground and Excited State Electronic Structure Calculations (7 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 interpolationAnil Damle Potentialities of wavelet formalism towards a reduction of the complexity of large scale electronic structure calculationsLuigi Genovese Convergence analysis for the EDIIS algorithmTim Kelley A Semi-smooth Newton Method For Solving semidefinite programs in electronic structure calculationsZaiwen Wen Adaptive compression for Hartree-Fock-like equationsMichael Lindsey Projected Commutator DIIS method for linear and nonlinear eigenvalue problemsLin Lin Parallel transport evolution of time-dependent density functional theoryDong An MS23 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 low-rank 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 low-rank 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 second-order methods on tensor manifolds, such as trust-region or quasi-Newton methods. It will also present results on dynamical approximation of tensor differential equations. Blind deconvolution by Optimizing over a Quotient ManifoldWen Huang Riemannian optimization and the computation of the divergences and the Karcher mean of symmetric positive definite matricesKyle A. Gallivan A manifold approach to structured low-rank matrix learningBamdev Mishra Subspace methods in Riemannian manifold optimizationWeihong Yang Quasi-Newton optimization methods on low-rank tensor manifoldsGennadij Heidel Robust second order optimization methods on low rank matrix and tensor varietiesValentin Khrulkov A Riemannian trust region method for the canonical tensor rank approximation problemNick Vannieuwenhoven Dynamical low-rank approximation of tensor differential equationsHanna Walach MS24 Parallel Sparse Triangular Solve on Emerging Platforms (4 talks) Weifeng Liu, Wei Xue 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 set-based methods (i.e., level-set and color-set) 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 next-generation SpTRSV algorithm design. Scalability Analysis of Sparse Triangular SolveWeifeng Liu Solving sparse triangular systems in GPUs: what are the options and how do I choose the right one?Ernesto Dufrechou Refactoring Sparse Triangular Solve on Sunway TaihuLight Many-core SupercomputerWei Xue Enhancing Scalability of Parallel Sparse Triangular Solve in SuperLUYang Liu MS25 Polynomial and Rational Matrices (7 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 Mini-Symposium 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; low-rank matrix pencils and matrix polinomials; block-tridiagonal linearizations. Stratifying complete eigenstructures: From matrix pencils to polynomials and backAndrii Dmytryshyn Block-symmetric linearizations of odd degree matrix polynomials with optimal condition number and backward errorMaria Isabel Bueno Transparent realizations for polynomial and rational matricesSteve Mackey Generic eigenstructures of matrix polynomials with bounded rank and degreeAndrii Dmytryshyn A geometric description of the sets of palindromic and alternating matrix pencils with bounded rankFernando De Terán Strong linearizations of rational matrices with polynomial part expressed in an orthogonal basisM. Carmen Quintana On the stability of the two-level orthogonal Arnoldi method for quadratic eigenvalue problemsJavier Pérez MS26 Preconditioners for fractional partial differentialequations and applications (4 talks) Daniele Bertaccini 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 ah-hoc 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 time-dependent fractional PDEsFabio Durastante Spectral analysis and multigrid preconditioners for space-fractional diffusion equationsMaria Rosa Mazza Fast tensor solvers for optimization problems with FDE-constraintsMartin Stoll Preconditioner for Fractional Diffusion Equations with Piecewise Continuous CoefficientsHai-wei Sun MS27 Preconditioners for ill-conditioned linear systems in large scale scientific computing (7 talks) Luca Bergamaschi, Massimiliano Ferronato, Carlo Janna The efficient solution to sparse linear systems is quite a common issue in several real world applications and often represents the main memory-and time-consuming task in a computer simulation. In many areas of large scale engineering and scientific computing, the solution to large, sparse and very ill-conditioned 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 state-of-the-art scalar and parallel preconditioning techniques with particular focus on 1. block preconditioners for indefinite systems 2. multilevel preconditioners 3. preconditionersfor least-squares problems 4. low-rank updates of preconditioners Robust AMG interpolation with target vectors for elasticity problemsRuipeng Li A Multilevel Preconditioner for Data Assimilation with 4D-VarAlison Ramage Algebraic Multigrid: theory and practiceJames Joseph Brannick Preconditioning for multi-physics problems: A general frameworkMassimiliano Ferronato Preconditioners for inexact-Newton methods based on compactrepresentation of Broyden class updatesJ.~Marín Preconditioning for Time-Dependent PDE-Constrained OptimizationJohn Pearson Spectral preconditioners for sequences of ill-conditioned linear systemsLuca Bergamaschi MS28 Preconditioning for PDE Constrained Optimization (4 talks) Roland Herzog, John Pearson The field of PDE-constrained optimization provides a gateway to the study of many real-world processes from science and industry. As these problems typically lead to huge-scale 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 multi-physics systems. In this minisymposium we wish to draw upon state-of-the-art 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 Kent-Andre Mardal Preconditioning for multiple saddle point problemsWalter Zulehner New Poisson-like preconditioners for fast and memory-efficient PDE-constrained optimizationLasse Hjuler Christiansen Preconditioning for Time-Dependent PDEs and PDE ControlAndrew Wathen MS29 Randomized algorithms for factorizing matrices (3 talks) Per-Gunnar Martinsson Methods based on randomized projections have over the last several years proven to provide powerful tools for computing low-rank 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 full factorizations of matrices, how to compute matrix factorizations where the factors are required to have non-negative 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 FactorizationsBenjamin Erichson Randomized algorithms for computing full rank-revealing factorizationsAbinand Gopal A randomized blocked algorithm for computing a rank-revealing UTV matrix decompositionNathan Heavner MS30 Rank structured methods for challenging numerical computations (8 talks) Sabine Le Borne, Jianlin Xia Rank-structured methods have demonstrated significant advantages in improving the efficiency and reliability of some large-scale computations and engineering simulations. These methods extend the fundamental ideas of multipole and panel-clustering methods to general non-local solution operators. While there exist various more or less closely related methods, the unifying aim of these methods is to explore efficient structured low-rank 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. H-matrices for stable computations in RBF interpolation problemsSabine Le Borne How good are H-Matrices at high frequencies?Timo Betcke Local low-rank approximation for the high-frequency Helmholtz equationSteffen Boerm Efficiency and Accuracy of Parallel Accumulator-based H-ArithmeticRonald Kriemann Analytical Compression via Proxy Point Selection and Contour IntegrationJianlin Xia The perfect shift and the fast computation of roots of polynomialsNicola Mastronardi Structured matrices in polynomial system solvingSimon Telen Preserving positive definiteness in HSS approximation and its application in preconditioningXin Xing MS31 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 algorithmSteven Elsworth Rational Krylov Subspaces for Wavefield ApplicationsJörn Zimmerling Krylov methods for Hermitian nonlinear eigenvalue problemsGiampaolo Mele Compressing variable-coefficient Helmholtz problems via RKFITStefan Güttel Rational Krylov methods in discrete inverse problemsVolker Grimm Inexact Rational Krylov methods applied to Lyapunov equationsMelina Freitag Numerical methods for Lyapunov matrix equations with banded symmetric dataDavide Palitta A comparison of rational Krylov and related low-rank methods for large Riccati equationsPatrick Kürschner MS32 Recent advances in linear algebra for uncertainty quantification (8 talks) Zhiwen Zhang, Bin Zheng The aim of this mini-symposium 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, multi-fidelity methods in uncertainty quantification, hierarchical matrices and low-rank 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 problemsZhongyi Huang An Adaptive Reduced Basis ANOVA Method for High-Dimensional Bayesian Inverse ProblemsQifeng Liao Randomized Kaczmarz method for linear inverse problemsYuling Jiao TBAJu Ming Sequential data assimilation with multiple nonlinear models and applications to subsurface flowPeng Wang A new model reduction technique for convection-dominated PDEs with random velocity fieldsGuannan Zhang Gamblet based multilevel decomposition/preconditioner for stochastic multiscale PDELei Zhang Scalable generation of spatially correlated random fieldsPanayot Vassilevski MS33 Recent Advances in Tensor Based Data Processing (8 talks) Chuan Chen, Yi Chang, Yao Wang, Xi-Le Zhao As a natural representation for high-dimensional 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 inter-disciplinary research field, there are fast emerging works on tensor based theory, models, numerical algorithms, and applications on data processing. This mini-symposium 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 ClusteringZi-Tai Chen Hyperspectral Image Restoration via Tensor-based Priors: From Low-rank to Deep ModelYi Chang Compressive Tensor Principal Component PursuitYao Wang Low-rank tensor completion using parallelmatrix factorization with factor priorsXi-Le Zhao Data Mining with Tensor based MethodsXu-Tao Li Low-rank Tensor Analysis with Noise ModelingZhi Han Hyperspectral and Multispectral Image Fusion Via Total Variation Regularized Nonlocal Tensor Train DecompositionKai-Dong Wang A Novel Tensor-based Video Rain Streaks Removal Approach via Utilizing Discriminatively Intrinsic PriorsLiang-Jian Deng MS34 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 real-world problems are analyzed by means of algebraic techniques that exploit low-rank 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 equationsStefano Massei RQZ: A rational QZ algorithm for the generalized eigenvalue problemDaan Camps Fast direct algorithms for least squares and least norm solutions for hierarchical matricesAbhay Gupta Computing the inverse matrix $phi_1$-function for a quasiseparable matrixLuca Gemignani The exact fine structure of the inverse of discrete elliptic linear operatorsShiv Chandrasekaran Fast direct solvers for boundary value problems on globally evolving geometriesAdrianna Gillman Matrix Aspects of Fast Multipole MethodXiaofeng Ou Adaptive Cross Approximation for Ill-Posed ProblemsThomas Mach MS35 Some recent applications of Krylov subspace methods (10 talks) Yunfeng Cai, Lei-Hong Zhang 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 real-world applications. Along this line, we propose this mini-symposium 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 mini-symposium, 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 ProblemsQiang Ye A block term decomposition of high order tensorsYunfeng Cai A Fast Implementation On The Exponential Marginal Fisher Analysis For High Dimensionality ReductionGang Wu Deflated block Krylov subspace methods for large scale eigenvalue problemsQiang Niu Lanczos type methods for the linear response eigenvalue problemZhongming Teng Sparse frequent direction algorithm for low rank approximationDelin Chu On the Generalized Lanczos Trust-Region MethodLei-Hong Zhang A Block Lanczos Method for the Extended Trust-Region SubproblemsWeihong Yang Parametrized quasi-soft thresholding operator for compressed sensing and matrix completionAn-Bao Xu Two-level RAS preconditioners of Krylov subspace methods for large sparse linear systemsXin Lu MS36 Tensor Analysis, Computation, and Applications I (8 talks) Weiyang Ding The term {it tensor} has both meanings of a geometric object and a multi-way 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 low-rank approximation, tensor spectral theory, tensor completion, tensor-related 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. Irreducible Function Bases of Isotropic Invariants of Third and Fourth Order Symmetric TensorsLiqun Qi The rank of $Wotimes W$ is eightShmuel Friedland Optimization methods using matrix and tensor structuresEugene Tyrtyshnikov Exploitation of structure in large-scale tensor decompositionsLieven De Lathauwer An Adaptive Correction Approach for Tensor CompletionMinru Bai Generalized polynomial complementarity problems with structured tensorsChen Ling Copositive Tensor Detection and Its Applications in Physics and HypergraphsHaibin Chen The bound of H-eigenvalue of some structure tensors with entries in an intervalLubin Cui MS37 Tensor Analysis, Computation, and Applications II (8 talks) Shenglong Hu The term {it tensor} has both meanings of a geometric object and a multi-way 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 low-rank approximation, tensor spectral theory, tensor completion, tensor-related 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 partitioningYannan Chen Solving tensor problems via continuation methodsLixing Han The Rank of $W \otimes W$ is EightShmuel Friedland Randomized Algorithms for the Approximations of Tucker and the Tensor Train Decomposition Maolin Che Sparse Tucker decomposition completion for 3D facial expression recognitionZiyan Luo Hankel Tensor Decompositions and RanksKe Ye Polytopes of Stochastic TensorsXiaodong Zhang Some Spectral Bounds and Properties on Non-Uniform Hypergraphs Chen Ouyang MS38 Tensor-Based Modelling (3 talks) Lieven De Lathauwer 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 channel-dependent signal-to-noise ratiosChuan Chen Tensor decompositions in reduced order modelsYoungsoo Choi Nonlinear system identification with tensor methodsKim Batselier MS39 Tensors and multilinear algebra (7 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 high-dimensional equations in numerical analysis. Higher-order tensors are a natural generalization of matrices and, just as for matrices, their low-rank 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 low-rank approximations. Adaptive Tensor Optimization for the Log-Normal Parametric Diffusion EquationMax Pfeffer Geometrical description of feasible singular values in tree tensor formatsSebastian Kraemer The positive cone to algebraic varieties of hierarchical tensorsBenjamin Kutschan Nuclear decomposition of higher-order tensorsLek-Heng Lim Duality of graphical models and tensor networksAnna Seigal Orthogonal tensors and rank-one approximation ratioAndre Uschmajew A condition number for the tensor rank decompositionNick Vannieuwenhoven MS40 The Perturbation Theory and Structure-Preserving Algorithms (9 talks) Zheng-Jian Bai, Tiexiang Li, Hanyu Li, Zhi-Gang Jia 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 eigenvector-dependent eigenvalue problem from solving the discrete Kohn-Sham equations.With a rigorous selection, we propose this mini-symposium 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 structure-preserving algorithms. The final aim of this mini-symposium 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 ApplicationsZhi-Gang Jia Improved random perturbation intervals of symmetric eigenvalue problemHanyu Li Error Bounds for Approximate Deflating Subspaces of Linear Response Eigenvalue ProblemsWei-Guo Wang Relative Perturbation Bounds for Eigenpairs of the Diagonalizable MatricesYanmei Chen Mixed and componentwise condition numbers for a linear function of the solution of the total least squares problemHuaian Diao Some perturbation results for Joint Block Diagonalization problemsDecai Shi A Structure-Preserving ${Gamma}$-Lanczos Algorithm for Bethe-Salpeter Eigenvalue ProblemsTiexiang Li A Structure-Preserving Jacobi Algorithm for Quaternion Hermitian Eigenvalue ProblemsRu-Ru Ma On the explicit expression of chordal metric between generalized singular values of Grassmann matrix pairs with applicationsWei-Wei Xu MS41 The Spectrum of Hypergraphs via Tensors (8 talks) Xiying Yuan 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 hypergraphsChangjiang Bu Some recent results on the tensor spectrum of hypergraphsAn Chang The spectral symmetry and stabilizing property of tensors and hypergraphsYizheng Fan Sharp upper and lower bounds for the spectral radius of a nonnegative weakly irreducible tensor and its applicationLihua You Some results on spectrum of graphsMei Lu Spectral Radius of ${0, 1}$-Tensor with Prescribed Number of OnesLinyuan Lu Some results in spectral (hyper)graph theoryXiaodong Zhang On distance Laplacian spectral radius of graphsBo Zhou MS42 Tridiagonal matrices and their applications in physics and mathematics (8 talks) Natalia Bebiano, Mikhail Tyaglov 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 pathsNatália Bebiano Tridiaglonal matrices with only one eigenvalue and their relations to polynomials orthogonal with non-Hermitian weightMikhail Tyaglov Positivity and Recursion formula of the linearization coefficients of Bessel polynomialsM. J. Atia Ultra-discrete analogue of the qd algorithm for Min-Plus tridiagonal matrixAkiko Fukuda A generalized eigenvalue problem with two tridiagonal matricesAlagacone Sri Ranga Eigenvalue problems of structured band matrices related to discrete integrable systemsMasato Shinjo On instability of the absolutely continuous spectrum of dissipative Schrödinger operators and Jacobi matricesRoman Romanov Block-tridiagonal linearizations of matrix polynomialsSusana Furtado