完全旋转高斯消去中生长因子的一个新的上界

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-02-26 DOI:10.1112/blms.70034

Ankit Bisain, Alan Edelman, John Urschel

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引用次数: 0

摘要

高斯消去法中的生长因子测量了一个LU分解的元素相对于原始矩阵的元素有多大。它是误差估计中的一个关键参数，也是数值分析中最基本的课题之一。我们给出了完全轴向-高斯消去中生长因子的上界n 0.2079 ln n +0.91 $n^{0.2079 \ln n +0.91}$这是对威尔金森1961年提出的2 n 0.25 ln n +0.5 $2 \, n ^{0.25\ln n +0.5}$的第一个改进。

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

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

The growth factor in Gaussian elimination measures how large the entries of an LU factorization can be relative to the entries of the original matrix. It is a key parameter in error estimates, and one of the most fundamental topics in numerical analysis. We produce an upper bound of $n^{0.2079 \ln n + 0.91}$ for the growth factor in Gaussian elimination with complete pivoting — the first improvement upon Wilkinson's original 1961 bound of $2 n^{0.25 \ln n + 0.5}$ .