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On Orthogonal Reduction to Hessenberg Form with Small Bandwidth

SYSNO ASEP	0314348
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	On Orthogonal Reduction to Hessenberg Form with Small Bandwidth
Title	O ortogonální redukci matice na pásovou Hessenbergovu matici
Author(s)	Faber, V. (US) Liesen, J. (DE) Tichý, Petr (UIVT-O)_{SAI, RID, ORCID}
Source Title	Numerical Algorithms. - : Springer - ISSN 1017-1398 Roč. 51, č. 2 (2009), s. 133-142
Number of pages	10 s.
Language	eng - English
Country	NL - Netherlands
Keywords	reduction to Hessenberg form ; Krylov subspace methods ; Arnoldi method ; Lanczos method
Subject RIV	BA - General Mathematics
R&D Projects	IAA100300802 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR)
CEZ	AV0Z10300504 - UIVT-O (2005-2011)
UT WOS	000265919800001
EID SCOPUS	67349189544
DOI	10.1007/s11075-008-9242-3
Annotation	Numerous algorithms in numerical linear algebra are based on the reduction of a given matrix A to a more convenient form. One of the most useful types of such reduction is the orthogonal reduction to (upper) Hessenberg form. This reduction can be computed by the Arnoldi algorithm. When A is Hermitian, the resulting upper Hessenberg matrix is tridiagonal. In this paper we study necessary and sufficient conditions on A so that the orthogonal Hessenberg reduction yields a Hessenberg matrix with small bandwidth. Our proof utilizes the idea of a "minimal counterexample", which is standard in combinatorial optimization, but rarely used in the context of linear algebra.
Workplace	Institute of Computer Science
Contact	Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800
Year of Publishing	2009

Number of the records: 1