Good pivots for small sparse matrices

Manuel Kauers; Jakob Moosbauer

doi:10.48550/arXiv.2006.01623

Good pivots for small sparse matrices

Research output: Working paper and reports › Preprint

Abstract

For sparse matrices up to size 8×8, we determine optimal choices for pivot selection in Gaussian elimination. It turns out that they are slightly better than the pivots chosen by a popular pivot selection strategy, so there is some room for improvement. We then create a pivot selection strategy using machine learning and find that it indeed leads to a small improvement compared to the classical strategy.

Original language	English
Number of pages	10
DOIs	https://doi.org/10.48550/arXiv.2006.01623
Publication status	Published - Jun 2020

Publication series

Name	arXiv.org
ISSN (Print)	2331-8422

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
102019 Machine learning

JKU Focus areas

Digital Transformation

Access to Document

10.48550/arXiv.2006.01623

Cite this

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title = "Good pivots for small sparse matrices",

abstract = "For sparse matrices up to size 8×8, we determine optimal choices for pivot selection in Gaussian elimination. It turns out that they are slightly better than the pivots chosen by a popular pivot selection strategy, so there is some room for improvement. We then create a pivot selection strategy using machine learning and find that it indeed leads to a small improvement compared to the classical strategy.",

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AB - For sparse matrices up to size 8×8, we determine optimal choices for pivot selection in Gaussian elimination. It turns out that they are slightly better than the pivots chosen by a popular pivot selection strategy, so there is some room for improvement. We then create a pivot selection strategy using machine learning and find that it indeed leads to a small improvement compared to the classical strategy.

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