On Best Approximations of Polynomials in Matrices in the Matrix 2-Norm

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F09%3A00330308" target="_blank" >RIV/67985807:_____/09:00330308 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

On Best Approximations of Polynomials in Matrices in the Matrix 2-Norm

Original language description

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 foruniqueness in these characterizations is not necessary.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/IAA100300802" target="_blank" >IAA100300802: Theory of Krylov subspace methods and its relationship to other mathematical disciplines</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2009

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

SIAM Journal on Matrix Analysis and Applications

ISSN

0895-4798

e-ISSN

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Volume of the periodical

31

Issue of the periodical within the volume

2

Country of publishing house

US - UNITED STATES

Number of pages

11

Pages from-to

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UT code for WoS article

000270196000004

EID of the result in the Scopus database

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