【数学学院】On an Eigenvector-Dependent Nonlinear Eigenvalue Problem

报告题目：On an Eigenvector-Dependent Nonlinear Eigenvalue Problem

报告人：Ren-cang Li

报告人单位：University of Texas at Arlington

报告时间：2018年7月24日上午10:00-

报告地点：数学学院西109

邀请人：刘长丽

摘要：

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 

$\sin\Theta$ 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.

来源链接：http://math.scu.edu.cn/info/1062/3585.htm