A new upper bound for the growth factor in Gaussian elimination with complete pivoting

Bisain, Ankit; Edelman, Alan; Urschel, John

A new upper bound for the growth factor in Gaussian elimination with complete pivoting

Name

Bulletin of London Math Soc - 2025 - Bisain - A new upper bound for the growth factor in Gaussian elimination with complete.pdf

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Published version

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sword-2025-10-15T17:25:59.original.xml (130 B)

Original SWORD entry document

Author(s)

Bisain, Ankit

•

Edelman, Alan

•

Urschel, John

Date Issued

February 26, 2025

Journal

Bulletin of the London Mathematical Society

Publisher

Wiley

Citation

Bisain, A., Edelman, A. and Urschel, J. (2025), A new upper bound for the growth factor in Gaussian elimination with complete pivoting. Bull. London Math. Soc., 57: 1369-1387.

Version

Final published version

Abstract

The growth factor in Gaussian elimination measureshow large the entries of an LU factorization can be rel-ative to the entries of the original matrix. It is a keyparameter in error estimates, and one of the most fun-damental topics in numerical analysis. We produce anupper bound of 𝑛 0.2079 ln 𝑛+0.91 for the growth factor inGaussian elimination with complete pivoting — the firstimprovement upon Wilkinson’s original 1961 bound of2 𝑛 0.25 ln 𝑛+0.5.

MIT Department

Massachusetts Institute of Technology. Department of Mathematics

Terms of Use

Creative Commons Attribution

https://creativecommons.org/licenses/by/4.0/

Persistent DSpace Link

https://hdl.handle.net/1721.1/163173

DOI of Published Version

https://doi.org/10.1112/blms.70034