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.


Linear Algebra Positive Definite Matrix Compute Solution Cholesky Decomposition Cholesky Factorization 
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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.MathSciNetzbMATHCrossRefGoogle 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.zbMATHGoogle Scholar
  3. [3]
    Wilkinson, J. H The algebraic eigenvalue problem. London: Oxford University Press 1965.zbMATHGoogle 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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