|Title: On an Eigenvector-Dependent Nonlinear Eigenvalue Problem|
|Seminar: Numerical Analysis and Scientific Computing|
|Speaker: Ren-Cang Li of University of Texas at Arlington|
|Contact: Yuanzhe Xi, email@example.com|
|Date: 2019-04-05 at 2:00PM|
|Venue: MSC W301|
We first establish existence and uniqueness conditions for the solvability of an algebraic eigenvalue problem with eigenvector nonlinearity. We then present a local and global convergence analysis for a self-consistent field (SCF) iteration for solving the problem. The well-known sin? theorem in the perturbation theory of Hermitian matrices plays a central role. The near-optimality of the local convergence rate of the SCF iteration is demonstrated by examples from the discrete Kohn-Sham eigenvalue problem in electronic structure calculations and the maximization of the trace ratio in the linear discriminant analysis for dimension reduction. This is a joint work with Yunfeng Cai (Peking University), Lei-Hong Zhang (Shanghai University of Finance and Economics), Zhaojun Bai (University of California at Davis).
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