On a self-consistent-field-like iteration for maximizing the sum of the Rayleigh quotients

作者：

Highlights：

• A self-consistent-field method for optimizing the sum of the Rayleigh quotients is proposed.

• Local convergence and global convergence are established under some conditions.

• Quadratic convergence is proved for some situations.

• Numerical testing shows efficiency, in comparison with other optimization-based methods.

摘要

•A self-consistent-field method for optimizing the sum of the Rayleigh quotients is proposed.•Local convergence and global convergence are established under some conditions.•Quadratic convergence is proved for some situations.•Numerical testing shows efficiency, in comparison with other optimization-based methods.

论文关键词：65F15,65K05,65F30,15A18,Rayleigh quotient,The nonlinear eigenvalue problem,The self-consistent-field iteration,Trust region

论文评审过程：Received 22 March 2012, Revised 10 July 2013, Available online 21 August 2013.

论文官网地址：https://doi.org/10.1016/j.cam.2013.08.005