Matrices with Tunable Infinity-Norm Condition Number and No Need for Pivoting in LU Factorization

Fasi, Massimiliano and Higham, Nicholas J. (2020) Matrices with Tunable Infinity-Norm Condition Number and No Need for Pivoting in LU Factorization. [MIMS Preprint]

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Abstract

We propose a two-parameter family of nonsymmetric dense n ⨉ n matrices A(α, β) for which LU factorization without pivoting is numerically stable, and we show how to choose α and β to achieve any value of the ∞-norm condition number. The matrix A(α, β) can be formed from a simple formula in O(n²) flops. The matrix is suitable for use in the HPL-AI Mixed-Precision Benchmark, which requires an extreme scale test matrix (dimension n > 10⁷) that has a controlled condition number and can be safely used in LU factorization without pivoting. It is also of interest as a general-purpose test matrix.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Mr Massimiliano Fasi
Date Deposited: 01 Aug 2020 14:08
Last Modified: 01 Aug 2020 14:09
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2775

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