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

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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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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  • AMS Subject Classifications: 68F05, 68G05.
  • Key Words: Gauss–Jordan algorithm, backward error analysis.