Rayleigh Quotient Optimizations and Eigenvalue Problems

Professor Zhaojun Bai

Professor of Computer Science and Mathematics, University of California, Davis
Faculty Scientist of Scalable Solvers Group, Lawrence Berkeley National Laboratory

Biography:
Zhaojun Bai is a Distinguished Professor in the Department of Computer Science
and Department of Mathematics, University of California, Davis, and a Faculty
Computer Scientist at Lawrence Berkeley National Laboratory. He obtained his PhD
from Fudan University, China and postdoctoral fellowship from Courant Institute,
New York University. His main research interests include linear algebra algorithm
design and analysis, mathematical software engineering and applications in
computational science and engineering, and data science. He participated in a
number of synergistic projects, such as LAPACK. He is an Editor-in-Chief of ACM
TOMS, and serves on editorial boards of JCM and Science China Mathematics
among others. Previously, he served as an associate editor of SIMAX, vice chair of
IEEE IPDPS and numerous other professional positions. He is a Fellow of SIAM.

Many computational science and data analysis techniques lead to optimizing Rayleigh quotient
(RQ) and RQ-type objective functions, such as computing excitation states (energies) of
electronic structures, robust classification to handle uncertainty and constrained data clustering
to incorporate domain knowledge. We will discuss emerging RQ optimization problems,
variational principles, and reformulations to algebraic linear and nonlinear eigenvalue
problems. We will show how to exploit underlying properties of these eigenvalue problems for
designing fast eigensolvers, and illustrate the efficacy of these solvers in applications.