CONVERGENCE ANALYSIS OF A BLOCK PRECONDITIONED STEEPEST DESCENT EIGENSOLVER WITH IMPLICIT DEFLATION

作     者：Zhou, Ming Bai, Zhaojun Cai, Yunfeng Neymeyr, Klaus 

作者机构：Universität Rostock Institut für Mathematik Ulmenstraße 69 Rostock18055 Germany Department of Computer Science Department of Mathematics University of California DavisCA95616 United States Cognitive Computing Lab Baidu Research No. 10 Xibeiwang East Road Beijing100193 China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2022年

核心收录：

主　　题：Steepest descent method 

摘      要：Gradient-type iterative methods for solving Hermitian eigenvalue problems can be accelerated by using preconditioning and deflation techniques. A preconditioned steepest descent iteration with implicit deflation (PSD-id) is one of such methods. The convergence behavior of the PSD-id is recently investigated based on the pioneering work of Samokish on the preconditioned steepest descent method (PSD). The resulting non-asymptotic estimates indicate a superlinear convergence of the PSD-id under strong assumptions on the initial guess. The present paper utilizes an alternative convergence analysis of the PSD by Neymeyr under much weaker assumptions. We embed Neymeyr’s approach into the analysis of the PSD-id using a restricted formulation of the PSD-id. More importantly, we extend the new convergence analysis of the PSD-id to a practically preferred block version of the PSD-id, or BPSD-id, and show the cluster robustness of the BPSD-id. Numerical examples are provided to validate the theoretical *** Codes 65F15, 65N12, 65N25 © 2022, CC BY-NC-ND.