完全旋转高斯消去中生长因子的一个新的上界

arXiv - CS - Numerical Analysis Pub Date : 2023-12-02 DOI:arxiv-2312.00994

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衡量的是，相对于原始矩阵的元素，LU分解的元素有多大。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。我们为高斯消去中具有完全轴向的生长因子产生了$n^{0.2079 \ln n+ 0.91}$的上界——这是对Wilkinson在1961年提出的$2 \，n^{0.25\ln n+0.5}$上界的第一次改进。

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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 $2 \, n ^{0.25\ln n +0.5}$.

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arXiv - CS - Numerical Analysis

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