On the Robustness of Gaussian Elimination with Partial Pivoting
- Paola FavatiAffiliated withIstituto di Matematica Computazionale del CNR
- , Mauro LeonciniAffiliated withFacoltà di Economia di Foggia, Università di BariIMC-CNR
- , Angeles MartinezAffiliated withDepartamento de Matemática Aplicada, Universidad Politécnica de Valencia
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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.
- On the Robustness of Gaussian Elimination with Partial Pivoting
BIT Numerical Mathematics
Volume 40, Issue 1 , pp 62-73
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- Kluwer Academic Publishers
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- Gaussian elimination
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- Author Affiliations
- 1. Istituto di Matematica Computazionale del CNR, Via S. Maria 46, 56126, Pisa, Italy
- 2. Facoltà di Economia di Foggia, Università di Bari, Via IV Novembre 1, 71100, Foggia, Italy
- 3. IMC-CNR, Via S. Maria 46, 56126, Pisa, Italy.
- 4. Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, 46071, Valencia, Spain.