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  • Článek analyzuje numerické chování některých výpočetních variant Gram-Schmidtova ortogonalizačního procesu. Zaměřuje se na studium ortogonality mezi vypočtenými vektory, která může být významně porušena zejména v klasické nebo modifikované variantě tohoto procesu. Na druhé straně je zachována na úrovni strojové přesnosti v Gram-Schmidtově procesu s reortogonalizací. Důsledky pro praktickou implementaci v paralelním prostředí jsou studovány v závěru publikace. (cs)
  • In this paper we study numerical behavior of several computational variants of the Gram-Schmidt orthogonalization process. We focus on the orthogonality of computed vectors which may be significantly lost in the classical or modified Gram-Schmidt algorithm, while the Gram-Schmidt algorithm with reorthogonalization has been shown to compute vectors which are orthogonal to machine precision level. The implications for practical implementation and its impact on the efficiency in the parallel computer environment are considered.
  • In this paper we study numerical behavior of several computational variants of the Gram-Schmidt orthogonalization process. We focus on the orthogonality of computed vectors which may be significantly lost in the classical or modified Gram-Schmidt algorithm, while the Gram-Schmidt algorithm with reorthogonalization has been shown to compute vectors which are orthogonal to machine precision level. The implications for practical implementation and its impact on the efficiency in the parallel computer environment are considered. (en)
Title
  • On the Loss of Orthogonality in the Gram-Schmidt Orthogonalization Process
  • O ztrátě ortogonality v klasickém Gram-Schmidtově ortogonalizačním procesu (cs)
  • On the Loss of Orthogonality in the Gram-Schmidt Orthogonalization Process (en)
skos:prefLabel
  • On the Loss of Orthogonality in the Gram-Schmidt Orthogonalization Process
  • O ztrátě ortogonality v klasickém Gram-Schmidtově ortogonalizačním procesu (cs)
  • On the Loss of Orthogonality in the Gram-Schmidt Orthogonalization Process (en)
skos:notation
  • RIV/67985807:_____/05:00404788!RIV06-AV0-67985807
http://linked.open.../vavai/riv/strany
  • 1069;1075
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  • P(1ET400300415), Z(AV0Z10300504)
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  • -
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  • 534479
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  • RIV/67985807:_____/05:00404788
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  • numerical linear algebra; QR factorization; Gram-Schmidt orthogonalization; reorthogonalization; rounding error analysis (en)
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  • GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV
  • [DCBA5D7EA303]
http://linked.open...i/riv/nazevZdroje
  • Computers & Mathematics With Applications
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  • 50
http://linked.open...iv/tvurceVysledku
  • Rozložník, Miroslav
  • Giraud, L.
  • Langou, J.
http://linked.open...n/vavai/riv/zamer
issn
  • 0898-1221
number of pages
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