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

We propose a two-parameter family of nonsymmetric dense $n\times n$ matrices $A(\alpha,\beta)$ for which LU factorization without pivoting is numerically stable, and we show how to choose $\alpha$ and $\beta$ to achieve any value of the $\infty$-norm condition number. The matrix $A(\alpha,\beta)$ can be formed from a simple formula in $O(n^2)$ flops. The matrix is suitable for use in the HPL-AI Mixed-Precision Benchmark, which requires an extreme scale test matrix (dimension $n>10^7$) 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.


Read More: https://epubs.siam.org/doi/abs/10.1137/20M1357238

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS; Vol.42 No.1 January-March 2021

No. Panggil

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Penerbit

: .,

Deskripsi Fisik

p. 417 - 435

Bahasa

English

ISBN/ISSN

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Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

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Subjek

LU FACTORIZATION
TEST MATRIX
INFTY-NORM CONDITION NUMBER
HPL-AI MIXED-PRECISION BENCHMARK
LOW-PRECISION ARITHMETIC

Info Detail Spesifik

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Pernyataan Tanggungjawab

Massimiliano Fasi, Nicholas J. Higham

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