A new framework for implicit restarting of the Krylov-Schur algorithm

作     者：Bujanovic, Zvonimir Drmac, Zlatko 

作者机构：Max Planck Inst Dynam Complex Tech Syst Magdeburg Germany Univ Zagreb Dept Math Zagreb 10000 Croatia 

出 版 物：《NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS》 (数值线性代数及其应用)

年 卷 期：2015年第22卷第2期

页      面：220-232页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Croatian MZOS [0372783-2750] Croatian Science Foundation 

主　　题：eigenvalues eigenvalue assignment Arnoldi algorithm Krylov-Schur algorithm implicit restart polynomial filter QR algorithm Rayleigh quotient Ritz values 

摘      要：This paper introduces a new framework for implicit restarting of the Krylov-Schur algorithm. It is shown that restarting with arbitrary polynomial filter is possible by reassigning some of the eigenvalues of the Rayleigh quotient through a rank-one correction, implemented using only the elementary transformations (translation and similarity) of the Krylov decomposition. This framework includes the implicitly restarted Arnoldi (IRA) algorithm and the Krylov-Schur algorithm with implicit harmonic restart as special cases. Further, it reveals that the IRA algorithm can be turned into an eigenvalue assignment method. Copyright (c) 2014 John Wiley & Sons, Ltd.