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Rounding Error Analysis of the Classical Gram-Schmidt Orthogonalization Process
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SYSNO ASEP 0405259 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Rounding Error Analysis of the Classical Gram-Schmidt Orthogonalization Process Title Analýza zaokrouhlovacích chyb klasického Gram-Schmidtova ortogonalizačního procesu Author(s) Giraud, L. (FR)
Langou, J. (FR)
Rozložník, Miroslav (UIVT-O) SAI, RID, ORCID
van den Eshof, J. (NL)Source Title Numerische Mathematik - ISSN 0029-599X
Roč. 101, - (2005), s. 87-100Number of pages 14 s. Language eng - English Country DE - Germany Keywords rounding error analysis ; orthogonalization ; classical Gram-Schmidt process Subject RIV BA - General Mathematics R&D Projects 1ET400300415 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) IAA1030405 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000230347000004 EID SCOPUS 22344449775 DOI 10.1007/s00211-005-0615-4 Annotation This paper provides two results on the numerical behavior of the classical Gram-Schmidt algorithm. The first result states that, provided the normal equations associated with the initial vectors are numerically nonsingular, the loss of orthogonality of the vectors computed by the classical Gram-Schmidt algorithm depends quadratically on the condition number of the initial vectors. The second result states that, provided the initial set of vectors has numerical full rank, two iterations of the classical Gram-Schmidt algorithm are enough for ensuring the orthogonality of the computed vectors to be close to the unit roundoff level. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2006
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