Reducing the amount of pivoting in symmetric indefinite systems

Authors:
Dulceneia Becker;Marc Baboulin;Jack Dongarra
Affiliations:
University of Tennessee;INRIA / Université Paris-Sud, France;University of Tennessee, Oak Ridge National Laboratory, University of Manchester, United Kingdom
Venue:
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part I
Year:
2011

Citing 7
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Abstract

This paper illustrates how the communication due to pivoting in the solution of symmetric indefinite linear systems can be reduced by considering innovative approaches that are different from pivoting strategies implemented in current linear algebra libraries. First a tiled algorithm where pivoting is performed within a tile is described and then an alternative to pivoting is proposed. The latter considers a symmetric randomization of the original matrix using the so-called recursive butterfly matrices. In numerical experiments, the accuracy of tile-wise pivoting and of the randomization approach is compared with the accuracy of the Bunch-Kaufman algorithm.