Iterative Refinement of the Solution of a Positive Definite System of Equations

  • R. S. Martin
  • G. Peters
  • J. H. Wilkinson
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 186)


In an earlier paper in this series [1] the solution of a system of equations Ax=b with a positive definite matrix of coefficients was described; this was based on the Cholesky factorization of A. If A is ill-conditioned the computed solution may not be sufficiently accurate, but (provided A is not almost singular to working accuracy) it may be improved by an iterative procedure in which the Cholesky decomposition is used repeatedly.




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  1. [1]
    Martin, R. S., G. Peters, and J. H. Wilkinson. Symmetric decompositions of a positive definite matrix. Numer. Math. 7, 362–383 (1965). Cf. I/1.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Wilkinson, J. H.: Rounding errors in algebraic processes. London: Her Majesty’s Stationary Office; Englewood Cliffs, N.J.: Prentice-Hall 1963. German edition: Rundungsfehler. Berlin-Göttingen-Heidelberg: Springer 1969.MATHGoogle Scholar
  3. [3]
    Wilkinson, J. H The algebraic eigenvalue problem. London: Oxford University Press 1965.MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1971

Authors and Affiliations

  • R. S. Martin
  • G. Peters
  • J. H. Wilkinson

There are no affiliations available

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