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On the Convergence of Q-OR and Q-MR Krylov Methods for Solving Nonsymmetric Linear Systems
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SYSNO ASEP 0454997 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On the Convergence of Q-OR and Q-MR Krylov Methods for Solving Nonsymmetric Linear Systems Author(s) Duintjer Tebbens, Jurjen (UIVT-O) RID, SAI, ORCID
Meurant, G. (FR)Source Title Bit. - : Springer - ISSN 0006-3835
Roč. 56, č. 1 (2016), s. 77-97Number of pages 21 s. Language eng - English Country SE - Sweden Keywords Krylov method ; Q-OR method ; Q-MR method ; BiCG ; QMR ; CMRH ; eigenvalue influence ; prescribed convergence Subject RIV BA - General Mathematics R&D Projects GA13-06684S GA ČR - Czech Science Foundation (CSF) Institutional support UIVT-O - RVO:67985807 UT WOS 000374411400005 EID SCOPUS 84952935275 DOI 10.1007/s10543-015-0564-y Annotation This paper addresses the convergence behavior of Krylov methods for nonsymmetric linear systems which can be classified as quasi-orthogonal (Q-OR) or quasi-minimum residual (Q-MR) methods. It explores, more precisely, whether the influence of eigenvalues is the same when using non-orthonormal bases as it is for the FOM and GMRES methods. It presents parametrizations of the classes of matrices with a given spectrum and right-hand sides generating prescribed Q-OR/Q-MR (quasi) residual norms and discusses non-admissible residual norm sequences. It also gives closed-form expressions of the Q-OR/Q-MR (quasi) residual norms as functions of the eigenvalues and eigenvectors of the matrix of the linear system. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2017
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