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Round off error analysis for Gram-Schmidt method and solution of linear least squares problems

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Abstract

Round off error analysis for the classical Gram-Schmidt orthogonalization method with re-orthogonalization is presented. The effect of the round-off error on the orthogonality of the derived vectors and also on the solution of the linear least squares problems when solved by the Gram-Schmidt algorithm are given. Numerical results compared favorably with the results of other methods. The classical case when no re-orthogonalization takes place is also discussed.

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Authors and Affiliations

  1. Computation Centre, National Research Council, Ottawa, Canada

    Nabih N. Abdelmalek

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  1. Nabih N. Abdelmalek
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Abdelmalek, N.N. Round off error analysis for Gram-Schmidt method and solution of linear least squares problems. BIT 11, 345–367 (1971). https://doi.org/10.1007/BF01939404

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  • DOI: https://doi.org/10.1007/BF01939404

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