Inversion of Positive Definite Matrices by the Gauss-Jordan Method

  • F. L. Bauer
  • C. Reinsch
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 186)


Let A be a real n×n matrix and
$$y = Ax$$
the induced mapping R nR n. If a 1,1ǂ0, then one can solve the first of these equations for x 1 and insert the result into the remaining equations.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bauer, F. L., Heinhold, J., Samelson, K., Sauer, R.: Moderne Rechenanlagen. Stuttgart: Teubner 1965.zbMATHGoogle Scholar
  2. 2.
    Bauer, F. L.: Genauigkeitsfragen bei der Lösung linearer Gleichungssysteme. Z. Angew. Math. Mech. 46, 409–421 (1966).MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Martin, R. S., Peters, G., Wilkinson, J. H.: Symmetrie decomposition of a positive definite matrix. Numer. Math. 7, 362–383 (1965). Cf. I/l.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Martin, R. S., Peters, G., Wilkinson, J. H. Iterative refinement of the solution of a positive definite system of equations. Numer. Math. 8, 203–216 (1966). Cf. 1/2.MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Rutishauser, H.: Automatische Rechenplanfertigung für programmgesteuerte Rechenanlagen. Z. Angew. Math. Phys. 3, 312–316 (1952).MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Petrie, G. W., III: Matrix inversion and solution of simultaneous linear algebraic equations with the IBM 604 Electronic Calculating Punch. Simultaneous linear equations and eigenvalues. Nat. Bur. Standards Appl. Math. Ser. 29, 107–112 (1953).MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1971

Authors and Affiliations

  • F. L. Bauer
  • C. Reinsch

There are no affiliations available

Personalised recommendations