BIT Numerical Mathematics

, Volume 40, Issue 1, pp 62–73 | Cite as

On the Robustness of Gaussian Elimination with Partial Pivoting

  • Paola Favati
  • Mauro Leoncini
  • Angeles Martinez
Article

Abstract

It has been recently shown that large growth factors might occur in Gaussian Elimination with Partial Pivoting (GEPP) also when solving some plausibly natural systems. In this note we argue that this potential problem could be easily solved, with much smaller risk of failure, by very small (and low cost) modifications of the basic algorithm, thus confirming its inherent robustness. To this end, we first propose an informal model with the goal of providing further support to the comprehension of the stability properties of GEPP. We then report the results of numerical experiments that confirm the viewpoint embedded in the model. Basing on the previous observations, we finally propose a simple scheme that could be turned into (even more) accurate software for the solution of linear systems.

Gaussian elimination stability pivoting 

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Copyright information

© Swets & Zeitlinger 2000

Authors and Affiliations

  • Paola Favati
    • 1
  • Mauro Leoncini
    • 2
    • 3
  • Angeles Martinez
    • 4
  1. 1.Istituto di Matematica Computazionale del CNRPisaItaly
  2. 2.Facoltà di Economia di FoggiaUniversità di BariFoggiaItaly
  3. 3.IMC-CNRPisaItaly.
  4. 4.Departamento de Matemática AplicadaUniversidad Politécnica de ValenciaValenciaSpain.

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