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  • This paper shows that the lower bound for the A-norm of the error based on Gauss quadrature is mathematically equivalent to the formula given by Hestenes and Stiefel. It compares existing bounds and demonstrates necessity of a proper rounding error analysis. It is given an example of the well-known bound which can fail in finite precision arithmetic. The simplest bound is proved numerically stable. Results are illustrated by numerical experiments.
  • This paper shows that the lower bound for the A-norm of the error based on Gauss quadrature is mathematically equivalent to the formula given by Hestenes and Stiefel. It compares existing bounds and demonstrates necessity of a proper rounding error analysis. It is given an example of the well-known bound which can fail in finite precision arithmetic. The simplest bound is proved numerically stable. Results are illustrated by numerical experiments. (en)
Title
  • On Error Estimation in the Conjugate Gradient Method and why it Works in Finite Precision Computations.
  • On Error Estimation in the Conjugate Gradient Method and why it Works in Finite Precision Computations. (en)
skos:prefLabel
  • On Error Estimation in the Conjugate Gradient Method and why it Works in Finite Precision Computations.
  • On Error Estimation in the Conjugate Gradient Method and why it Works in Finite Precision Computations. (en)
skos:notation
  • RIV/67985807:_____/02:06020143!RIV/2003/AV0/A06003/N
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  • 56;80
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  • P(GA201/02/0595), Z(AV0Z1030915)
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  • RIV/67985807:_____/02:06020143
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  • conjugate gradient method; Gauss kvadrature; evaluation of convergence; error bounds; finite precision arithmetic; rounding errors; loss of orthogonality (en)
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  • [FBB4BE6A4231]
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  • 13
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  • Strakoš, Zdeněk
  • Tichý, Petr
http://linked.open...n/vavai/riv/zamer
issn
  • 1068-9613
number of pages
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