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

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

{"title":"A new upper bound for the growth factor in Gaussian elimination with complete pivoting","authors":"Ankit Bisain, Alan Edelman, John Urschel","doi":"10.1112/blms.70034","DOIUrl":null,"url":null,"abstract":"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 <math>\n <semantics>\n <msup>\n <mi>n</mi>\n <mrow>\n <mn>0.2079</mn>\n <mi>ln</mi>\n <mi>n</mi>\n <mo>+</mo>\n <mn>0.91</mn>\n </mrow>\n </msup>\n <annotation>$n^{0.2079 \\ln n +0.91}$</annotation>\n </semantics></math> for the growth factor in Gaussian elimination with complete pivoting — the first improvement upon Wilkinson's original 1961 bound of <math>\n <semantics>\n <mrow>\n <mn>2</mn>\n <mspace></mspace>\n <msup>\n <mi>n</mi>\n <mrow>\n <mn>0.25</mn>\n <mi>ln</mi>\n <mi>n</mi>\n <mo>+</mo>\n <mn>0.5</mn>\n </mrow>\n </msup>\n </mrow>\n <annotation>$2 \\, n ^{0.25\\ln n +0.5}$</annotation>\n </semantics></math>.","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 5","pages":"1369-1387"},"PeriodicalIF":0.8000,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70034","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/blms.70034","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

Abstract

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

Abstract Image

查看原文本刊更多论文

完全旋转高斯消去中生长因子的一个新的上界

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊