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Pivoting techniques for symmetric Gaussian elimination

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Summary

In order to factorize an indefinite symmetric matrixG of the formG=LDL T whereL is a trivially invertible matrix andD is a diagonal matrix, we introduce a new kind of pivoting operation. The algorithm suggested maintains the stability and efficiency of the standard Cholesky decomposition whileG need not be positive definite. The problem of factorizingG+αuu T whereu is a vector, α scalar and the factors ofG are known, is also discussed.

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    A. Dax & S. Kaniel

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  1. A. Dax
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  2. S. Kaniel
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This research was supported in part by the Israeli National Council for Research and Development

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Dax, A., Kaniel, S. Pivoting techniques for symmetric Gaussian elimination. Numer. Math. 28, 221–241 (1977). https://doi.org/10.1007/BF01394454

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  • DOI: https://doi.org/10.1007/BF01394454

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