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Main Title: On best approximations of polynomials in matrices in the matrix 2-norm
Author(s): Liesen, Jörg
Tichý, Petr
Type: Article
Language Code: en
Abstract: 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.
Issue Date: 30-Jul-2009
Date Available: 19-Dec-2017
DDC Class: 515 Analysis
512 Algebra
Subject(s): matrix approximation problems
polynomials in matrices
matrix functions
matrix 2-norm
Arnoldi’s method
Journal Title: SIAM Journal on Matrix Analysis and Applications
Publisher: Society for Industrial and Applied Mathematics
Publisher Place: Philadelphia, Pa
Volume: 31
Issue: 2
Publisher DOI: 10.1137/080728299
Page Start: 853
Page End: 863
EISSN: 1095-7162
ISSN: 0895-4798
Appears in Collections:FG Numerische Lineare Algebra » Publications

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