Prof. Zhaojun Bai, University of California Davis, will give a seminar with the title: Rayleigh quotient optimizations and eigenvalue problems.
Abstract: 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 a prior information. We will discuss origins of recently 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.
