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Statements

Subject Item
n2:RIV%2F67985807%3A_____%2F09%3A00330308%21RIV10-AV0-67985807
rdf:type
n8:Vysledek skos:Concept
dcterms: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 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.
dcterms: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
skos:prefLabel
On Best Approximations of Polynomials in Matrices in the Matrix 2-Norm On Best Approximations of Polynomials in Matrices in the Matrix 2-Norm
skos:notation
RIV/67985807:_____/09:00330308!RIV10-AV0-67985807
n3:aktivita
n14:P n14:Z
n3:aktivity
P(IAA100300802), Z(AV0Z10300504)
n3:cisloPeriodika
2
n3:dodaniDat
n10:2010
n3:domaciTvurceVysledku
n9:2085674
n3:druhVysledku
n12:J
n3:duvernostUdaju
n16:S
n3:entitaPredkladatele
n17:predkladatel
n3:idSjednocenehoVysledku
331336
n3:idVysledku
RIV/67985807:_____/09:00330308
n3:jazykVysledku
n13:eng
n3:klicovaSlova
matrix approximation problems; polynomials in matrices; matrix functions; matrix 2-norm; GMRES; Arnoldi's method
n3:klicoveSlovo
n5:matrix%20functions n5:GMRES n5:polynomials%20in%20matrices n5:matrix%202-norm n5:matrix%20approximation%20problems n5:Arnoldi%27s%20method
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[A4991D88A1D3]
n3:nazevZdroje
SIAM Journal on Matrix Analysis and Applications
n3:obor
n4:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n18:IAA100300802
n3:rokUplatneniVysledku
n10:2009
n3:svazekPeriodika
31
n3:tvurceVysledku
Liesen, J. Tichý, Petr
n3:wos
000270196000004
n3:zamer
n6:AV0Z10300504
s:issn
0895-4798
s:numberOfPages
11