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Solution of Symmetric and Unsymmetric Band Equations and the Calculations of Eigenvectors of Band Matrices

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

Abstract

In an earlier paper in this series [2] the triangular factorization of positive definite band matrices was discussed. With such matrices there is no need for pivoting, but with non-positive definite or unsymmetric matrices pivoting is necessary in general, otherwise severe numerical instability may result even when the matrix is well-conditioned.

Keywords

Notational Detail Rayleigh Quotient Band Matrix Band Matrice Inverse Iteration 
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References

  1. [1]
    Bowdler, H.J., R.S.Martin, G.Peters, and J.H.Wilkinson: Solution of Real and Complex Systems of Linear Equations. Numer. Math. 8, 217 -234 (1966). Cf. I/7.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    Martin, R. S., and J. H. Wilkinson. Symmetric decomposition of positive de-finite band matrices. Numer. Math. 7, 355 -361 (1965). Cf. I/4.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    Martin, R. S., and J. H. Wilkinson, G. Peters, and J. H. Wilkinson. Iterative refinement of the solution of a positive definite system of equations. Numer. Math. 8, 203–216 (1966). Cf. 1/2.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Peters, G., and J. H. Wilkinson. The calculation of specified eigenvectors by inverse iteration. Cf. II/18.Google Scholar
  5. [5]
    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
  • J. H. Wilkinson

There are no affiliations available

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