BIT Numerical Mathematics

, Volume 37, Issue 3, pp 687–705

Matrices, moments and quadrature II; How to compute the norm of the error in iterative methods

  • G. H. Golub
  • G. Meurant
Article

DOI: 10.1007/BF02510247

Cite this article as:
Golub, G.H. & Meurant, G. Bit Numer Math (1997) 37: 687. doi:10.1007/BF02510247
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Abstract

In this paper, we study the numerical computation of the errors in linear systems when using iterative methods. This is done by using methods to obtain bounds or approximations of quadratic formsuTA−1u whereA is a symmetric positive definite matrix andu is a given vector. Numerical examples are given for the Gauss-Seidel algorithm.

Moreover, we show that using a formula for theA-norm of the error from Dahlquist, Golub and Nash [1978] very good bounds of the error can be computed almost for free during the iterations of the conjugate gradient method leading to a reliable stopping criterion.

AMS subject classification

65F50

Key words

Iterative methodserror computationconjugate gradient

Copyright information

© BIT Foundation 1997

Authors and Affiliations

  • G. H. Golub
    • 1
  • G. Meurant
    • 2
  1. 1.Stanford UniversityComputer Science DepartmentStanfordUSA
  2. 2.CEA/Limeil-ValentonSt Georges CedexFrance