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A Note on the Stability of Gauss–Jordan Elimination for Diagonally Dominant Matrices

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Abstract

Peters and Wilkinson [2] state that “it is well known that Gauss–Jordan is stable” for a diagonally dominant matrix, but a proof does not seem to have been published [1]. The present note fills this gap. Gauss–Jordan elimination is backward stable for matrices diagonally dominant by rows and not for those diagonally dominant by columns. In either case it is forward stable.

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Authors and Affiliations

  1. Department of Informatics University of Bergen N-5020 Bergen, Norway e-mail: sasha@ii.uib.no, , , , , , NO

    A. N. Malyshev

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  1. A. N. Malyshev
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Received February 28, 2000

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Malyshev, A. A Note on the Stability of Gauss–Jordan Elimination for Diagonally Dominant Matrices. Computing 65, 281–284 (2000). https://doi.org/10.1007/s006070070012

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  • DOI: https://doi.org/10.1007/s006070070012

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