Solution of Real and Complex Systems of Linear Equations

  • H. J. Bowdler
  • R. S. Martin
  • G. Peters
  • J. H. Wilkinson
Part of the Handbook for Automatic Computation book series (HDBKAUCO, volume 2)

Abstract

If A is a non-singular matrix then, in general, it can be factorized in the form A = LU, where L is lower-triangular and U is upper-triangular. The factorization, when it exists, is unique to within a non-singular diagonal multiplying factor.

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References

  1. [1]
    Bauer, F. L.: Optimally scaled matrices. Numer. Math. 5, 73–87 (1963).MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    Forsythe, G. E.: Crout with pivoting. Comm. ACM 3, 507–508 (1960).CrossRefGoogle Scholar
  3. [3]
    Forsythe, G. E., and E. G. Straus: On best conditioned matrices. Proc. Amer. Math. Soc. 6, 340–345 (1955).MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    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.MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    Martin, R. S., 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. I/2.MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    McKeeman, W. M.: Crout with equilibration and iteration. Comm. ACM 5, 553–555 (1962).CrossRefGoogle Scholar
  7. [7]
    Wilkinson, J. H.: Rounding errors in algebraic processes. London: Her Majesty’s Stationery Office; Englewood Cliffs, N.J.: Prentice-Hall 1963. German edition: Rundungsfehler. Berlin-Göttingen-Heidelberg: Springer 1969.MATHGoogle Scholar
  8. [8]
    Wilkinson, J. H.: The algebraic eigenvalue problem. London: Oxford University Press 1965.MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1971

Authors and Affiliations

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

There are no affiliations available

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