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Symmetric Decomposition of Positive Definite Band Matrices

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

Abstract

The method is based on the following theorem. If A is a positive definite matrix of band form such that
$${a_{ij}} = 0{\rm{ (|}}i - j| >m{\rm{)}}$$
(1)
then there exists a real non-singular lower triangular matrix L such that
$$L{L^T} = A,{\rm{ where }}{l_{ij}} = 0{\rm{ (}}i - j >m{\rm{)}}{\rm{.}}$$
(2)

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References

  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. 1/1.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    Wilkinson, J. H.: The algebraic eigenvalue problem. London: Oxford University Press 1965.zbMATHGoogle Scholar
  3. [3]
    Rutishauser, H.: Solution of the eigenvalue problem with the LR transformation. Nat. Bur. Standards Appl. Math. Ser. 49, 47 – 81 (1958).MathSciNetGoogle Scholar
  4. [4]
    Ginsburg, T.: The conjugate gradient method. Numer. Math. 5, 191–200 (1963). Cf. 1/5.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1971

Authors and Affiliations

  • R. S. Martin
  • J. H. Wilkinson

There are no affiliations available

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