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

Author(s)
Bisain, Ankit; Edelman, Alan; Urschel, John
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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.
Date issued
2025-02-26
URI
https://hdl.handle.net/1721.1/163173
Department
Massachusetts Institute of Technology. Department of Mathematics
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.
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