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Rounding Error Analysis of the Classical Gram-Schmidt Orthogonalization Process

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    SYSNO ASEP0405259
    Document TypeJ - Journal Article
    R&D Document TypeJournal Article
    Subsidiary JČlánek ve WOS
    TitleRounding Error Analysis of the Classical Gram-Schmidt Orthogonalization Process
    TitleAnalýza 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 TitleNumerische Mathematik - ISSN 0029-599X
    Roč. 101, - (2005), s. 87-100
    Number of pages14 s.
    Languageeng - English
    CountryDE - Germany
    Keywordsrounding error analysis ; orthogonalization ; classical Gram-Schmidt process
    Subject RIVBA - General Mathematics
    R&D Projects1ET400300415 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)
    CEZAV0Z10300504 - UIVT-O (2005-2011)
    UT WOS000230347000004
    EID SCOPUS22344449775
    DOI10.1007/s00211-005-0615-4
    AnnotationThis 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.
    WorkplaceInstitute of Computer Science
    ContactTereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800
    Year of Publishing2006

Number of the records: 1  

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