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On Chebyshev Polynomials of Matrices
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SYSNO ASEP 0346245 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On Chebyshev Polynomials of Matrices Author(s) Faber, V. (US)
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. 4 (2010), s. 2205-2221Number of pages 17 s. Language eng - English Country US - United States Keywords matrix approximation problems ; Chebyshev polynomials ; complex approximation theory ; Krylov subspace methods ; Arnoldi's method Subject RIV BA - General Mathematics R&D Projects IAA100300802 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) Next source I CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000279347600034 EID SCOPUS 77956016661 DOI 10.1137/090779486 Annotation The mth Chebyshev polynomial of a square matrix A is the monic polynomial that minimizes the matrix 2-norm of p(A) over all monic polynomials p(z) of degree m. This polynomial is uniquely defined if m is less than the degree of the minimal polynomial of A. We study general properties of Chebyshev polynomials of matrices, which in some cases turn out to be generalizations of well-known properties of Chebyshev polynomials of compact sets in the complex plane. We also derive explicit formulas of the Chebyshev polynomials of certain classes of matrices, and explore the relation between Chebyshev polynomials of one of these matrix classes and Chebyshev polynomials of lemniscatic regions in the complex plane. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2011
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