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On Best Approximations of Polynomials in Matrices in the Matrix 2-Norm
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SYSNO ASEP 0330308 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On Best Approximations of Polynomials in Matrices in the Matrix 2-Norm Title O nejlepší aproximaci maticových polynomů ve 2-normě matice Author(s) Liesen, J. (DE)
Tichý, Petr (UIVT-O) SAI, RID, ORCIDSource Title SIAM Journal on Matrix Analysis and Applications. - : SIAM Society for Industrial and Applied Mathematics - ISSN 0895-4798
Roč. 31, č. 2 (2009), s. 853-863Number of pages 11 s. Language eng - English Country US - United States Keywords matrix approximation problems ; polynomials in matrices ; matrix functions ; matrix 2-norm ; GMRES ; Arnoldi's method Subject RIV BA - General Mathematics R&D Projects IAA100300802 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000270196000004 EID SCOPUS 72449126515 DOI 10.1137/080728299 Annotation We show that certain matrix approximation problems in the matrix 2-norm have uniquely defined solutions, despite the lack of strict convexity of the matrix 2-norm. The problems we consider are generalizations of the ideal Arnoldi and ideal GMRES approximation problems introduced by Greenbaum and Trefethen [SIAM J. Sci. Comput., 15 (1994), pp. 359-368]. We also discuss general characterizations of best approximation in the matrix 2-norm and provide an example showing that a known sufficient condition for uniqueness in these characterizations is not necessary. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2010
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