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Inversion of Positive Definite Matrices by the Gauss-Jordan Method

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Handbook for Automatic Computation

Part of the book series: Die Grundlehren der mathematischen Wissenschaften ((GL,volume 186))

Abstract

Let A be a real n×n matrix and

$$y = Ax$$
((1))

the induced mapping R n→R 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.

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References

  1. Bauer, F. L., Heinhold, J., Samelson, K., Sauer, R.: Moderne Rechenanlagen. Stuttgart: Teubner 1965.

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  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.

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  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.

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  5. Rutishauser, H.: Automatische Rechenplanfertigung für programmgesteuerte Rechenanlagen. Z. Angew. Math. Phys. 3, 312–316 (1952).

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  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).

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Authors
  1. F. L. Bauer
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  2. C. Reinsch
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Editor information

Editors and Affiliations

  1. Mathematisches Institut, Technichen Universität, 8 München 2, Arcisstr. 21, Deutschland

    F. L. Bauer

  2. Fachgruppe Computer-Wissenschaften, Eidgenössische Technische Hochschule Zürich, CH-8006, Zürich, Schweiz, Clausiusstr. 55

    H. Rutishauser

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© 1971 Springer-Verlag Berlin · Heidelberg

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Bauer, F.L., Reinsch, C. (1971). Inversion of Positive Definite Matrices by the Gauss-Jordan Method. In: Bauer, F.L., Householder, A.S., Olver, F.W.J., Rutishauser, H., Samelson, K., Stiefel, E. (eds) Handbook for Automatic Computation. Die Grundlehren der mathematischen Wissenschaften, vol 186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-86940-2_3

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  • DOI: https://doi.org/10.1007/978-3-642-86940-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-86942-6

  • Online ISBN: 978-3-642-86940-2

  • eBook Packages: Springer Book Archive

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