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

Jörg Liesen | Zendy; Petr Tichý | Zendy

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

Author(s) -

Jörg Liesen,

Petr Tichý

Publication year - 2009

Publication title -

siam journal on matrix analysis and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.268

H-Index - 101

eISSN - 1095-7162

pISSN - 0895-4798

DOI - 10.1137/080728299

Subject(s) - mathematics , norm (philosophy) , uniqueness , convexity , matrix (chemical analysis) , matrix norm , generalized minimal residual method , uniform norm , pure mathematics , algebra over a field , combinatorics , mathematical analysis , eigenvalues and eigenvectors , linear system , physics , quantum mechanics , political science , law , materials science , financial economics , economics , composite material

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

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