A Riemannian Optimization Approach for Solving the Generalized Eigenvalue Problem for Nonsquare Matrix Pencils

被引：7
作者：
Jiao-fen Li
Wen Li
Seak-Weng Vong
Qi-Lun Luo
MingQing Xiao
机构：
[1] Guilin University of Electronic Technology,School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation
[2] South China Normal University,School of Mathematical Sciences
[3] University of Macau,Department of Mathematics
[4] Southern Illinois University,Department of Mathematics
来源：
Journal of Scientific Computing | 2020年 / 82卷
关键词：
Generalized eigenvalue; Nonsquare pencils; Riemannian optimization; Stiefel manifold; 15A24; 15A18; 65F10; 65F15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, based on the Riemannian optimization approach we propose a Riemannian nonlinear conjugate gradient method with nonmonotone line search technique for solving the l parameterized original problem on generalized eigenvalue problems for nonsquare matrix pencils, which was first proposed by Chu and Golub (SIAM J Matrix Anal Appl 28:770–787, 2006). The new innovative approach is to reformulate the original optimization problem as a feasible optimization problem over a certain real product manifold. The global convergence of the proposed method is then established. Some numerical tests are given to demonstrate the efficiency of the proposed method. Comparisons with some latest methods are also given.
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