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  • 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.
  • 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. (en)
Title
  • On Best Approximations of Polynomials in Matrices in the Matrix 2-Norm
  • On Best Approximations of Polynomials in Matrices in the Matrix 2-Norm (en)
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  • On Best Approximations of Polynomials in Matrices in the Matrix 2-Norm
  • On Best Approximations of Polynomials in Matrices in the Matrix 2-Norm (en)
skos:notation
  • RIV/67985807:_____/09:00330308!RIV10-AV0-67985807
http://linked.open...avai/riv/aktivita
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  • P(IAA100300802), Z(AV0Z10300504)
http://linked.open...iv/cisloPeriodika
  • 2
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  • 331336
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  • RIV/67985807:_____/09:00330308
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  • matrix approximation problems; polynomials in matrices; matrix functions; matrix 2-norm; GMRES; Arnoldi's method (en)
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  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [A4991D88A1D3]
http://linked.open...i/riv/nazevZdroje
  • SIAM Journal on Matrix Analysis and Applications
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http://linked.open...UplatneniVysledku
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  • 31
http://linked.open...iv/tvurceVysledku
  • Tichý, Petr
  • Liesen, J.
http://linked.open...ain/vavai/riv/wos
  • 000270196000004
http://linked.open...n/vavai/riv/zamer
issn
  • 0895-4798
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