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 / P., Favati; Leoncini, Mauro; A., Martinez. - In: BIT. - ISSN 0006-3835. - STAMPA. - 40:(2000), pp. 62-73.

ON THE ROBUSTNESS OF GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING

LEONCINI, Mauro;
2000

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.
BIT
40
62
73
ON THE ROBUSTNESS OF GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING / P., Favati; Leoncini, Mauro; A., Martinez. - In: BIT. - ISSN 0006-3835. - STAMPA. - 40:(2000), pp. 62-73.
P., Favati; Leoncini, Mauro; A., Martinez
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/454038
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