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  • The Lanczos and conjugate gradient algorithms were introduced more than five decades ago. Because of their fundamental relationship with the theory of orthogonal polynomials and Gauss quadrature of Riemann-Stieltjes integral, they represent very interesting general mathematical objects, with highly nonlinear properties which can be conveniently translated from algebraic language into the language of mathematical analysis, and vice versa. Their numerical behaviour can be explained by an elegant mathematical theory.
  • The Lanczos and conjugate gradient algorithms were introduced more than five decades ago. Because of their fundamental relationship with the theory of orthogonal polynomials and Gauss quadrature of Riemann-Stieltjes integral, they represent very interesting general mathematical objects, with highly nonlinear properties which can be conveniently translated from algebraic language into the language of mathematical analysis, and vice versa. Their numerical behaviour can be explained by an elegant mathematical theory. (en)
  • Lanczosova metoda a metoda konjugovaných gradientů byly navrženy před více než padesáti lety. Vzhledem k jejich fundamentálnímu vztahu k teorii ortogonálních polynomů a Gaussovy kvadratury Reimann-Stieltjesova integrálu představují velmi zajímavé obecné matematické objekty s vysoce nelineárními vlastnostmi, které mohou být výhodně popisovány jak v jazyce analýzy tak v jazyce algebry. Jejich numerické chování může rovněž být popsáno elegantní matematickou teorií. (cs)
Title
  • The Lanczos and Conjugate Gradient Algorithms in Finite Precision Arithmetic
  • The Lanczos and Conjugate Gradient Algorithms in Finite Precision Arithmetic (en)
  • Lanczosova metoda a metoda konjugovaných gradientů v aritmetice s konečnou přesností (cs)
skos:prefLabel
  • The Lanczos and Conjugate Gradient Algorithms in Finite Precision Arithmetic
  • The Lanczos and Conjugate Gradient Algorithms in Finite Precision Arithmetic (en)
  • Lanczosova metoda a metoda konjugovaných gradientů v aritmetice s konečnou přesností (cs)
skos:notation
  • RIV/67985807:_____/06:00032220!RIV07-AV0-67985807
http://linked.open.../vavai/riv/strany
  • 471;542
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  • P(1ET400300415), Z(AV0Z10300504)
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  • 482862
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  • RIV/67985807:_____/06:00032220
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  • Lanczos method; conjugate gradient method; finite precision arithmetic; numerical stability; iterative methods (en)
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  • GB - Spojené království Velké Británie a Severního Irska
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  • [FA5008E93522]
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  • Acta Numerica
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  • 15
http://linked.open...iv/tvurceVysledku
  • Strakoš, Zdeněk
  • Meurant, G.
http://linked.open...n/vavai/riv/zamer
issn
  • 0962-4929
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