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A schmidt type process for the solution of Ax=b

Ein Prozeß vom Schmidt-Typus zur Lösung von Ax=b

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Abstract

An orthogonalization type algorithm is presented for the triangularization of the coefficient matrix of a system of linear algebraic equations. A backward error analysis is performed on the algorithm. Some numerical examples are presented. The algorithm is extended in order to perform the complete forward reduction.

Zusammenfassung

Ein Algorithmus vom Orthogonalisations-Typus wird für die Triangularisation einer Koeffizientenmatrix von linearen algebraischen Gleichungen abgeleitet. Eine rückwärts gerichtete Fehleranalyse wird an den Algorithmen vorgenommen. Es werden einige rechnerische Beispiele gegeben, und der Algorithmus wird erweitert, um eine vollständige, nach vorn gerichtete Reduktion vorzunehmen.

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References

  1. Westlake, J. R.: A handbook of matrix inversion and solution of linear equations. New York-London-Sydney: J. Wiley 1968.

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  2. Wilkinson, J. H.: Error analysis of direct methods of matrix inversion. J. Assoc. Comp. Mach.8, 281–330 (1961).

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  3. Wilkinson, J. H.: Rounding errors in algebraic processes. Notes on Applied Science No. 32. Her Majesty's Stationery Office, 1963.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of the Witwatersrand, 2001, Johannesburg, South Africa

    D. S. Henderson & C. J. Wright

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  1. D. S. Henderson
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  2. C. J. Wright
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Henderson, D.S., Wright, C.J. A schmidt type process for the solution of Ax=b. Computing 16, 231–237 (1976). https://doi.org/10.1007/BF02280882

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  • DOI: https://doi.org/10.1007/BF02280882

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