高相对精度计算两类符号正则矩阵乘积的特征值

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-11-13 DOI:10.1016/j.laa.2024.11.006

Xiaoxiao Ma , Yingqing Xiao , Zhao Yang

{"title":"高相对精度计算两类符号正则矩阵乘积的特征值","authors":"Xiaoxiao Ma , Yingqing Xiao , Zhao Yang","doi":"10.1016/j.laa.2024.11.006","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we consider how to accurately solve the product eigenvalue problem for the class of sign regular (SR) matrices with signature <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mn>1</mn><mo>,</mo><mo>−</mo><mn>1</mn><mo>)</mo></math></span> and the class of totally nonnegative (TN) matrices, which tend to be extremely ill-conditioned. We present algorithms with <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> complexity to accurately compute the parameter matrices of products of TN matrices and SR matrices with signature <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mn>1</mn><mo>,</mo><mo>−</mo><mn>1</mn><mo>)</mo></math></span>. Based on the accurate parameter matrices, all eigenvalues of the product matrix are computed to high relative accuracy. Numerical experiments are provided to confirm the claimed high relative accuracy.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"707 ","pages":"Pages 80-106"},"PeriodicalIF":1.0000,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Computing eigenvalues for products of two classes of sign regular matrices to high relative accuracy\",\"authors\":\"Xiaoxiao Ma , Yingqing Xiao , Zhao Yang\",\"doi\":\"10.1016/j.laa.2024.11.006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we consider how to accurately solve the product eigenvalue problem for the class of sign regular (SR) matrices with signature <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mo>⋯</mo><mo>,</mo><mn>1</mn><mo>,</mo><mo>−</mo><mn>1</mn><mo>)</mo></math></span> and the class of totally nonnegative (TN) matrices, which tend to be extremely ill-conditioned. We present algorithms with <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> complexity to accurately compute the parameter matrices of products of TN matrices and SR matrices with signature <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mn>1</mn><mo>,</mo><mo>−</mo><mn>1</mn><mo>)</mo></math></span>. Based on the accurate parameter matrices, all eigenvalues of the product matrix are computed to high relative accuracy. Numerical experiments are provided to confirm the claimed high relative accuracy.</div></div>\",\"PeriodicalId\":18043,\"journal\":{\"name\":\"Linear Algebra and its Applications\",\"volume\":\"707 \",\"pages\":\"Pages 80-106\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-11-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Linear Algebra and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0024379524004269\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Linear Algebra and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0024379524004269","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们考虑了如何精确求解签名为 (1,⋯,1,-1) 的符号正则（SR）矩阵和完全非负（TN）矩阵的乘积特征值问题。我们提出了复杂度为 O(n3) 的算法，可以精确计算 TN 矩阵和符号为 (1,...,1,-1) 的 SR 矩阵乘积的参数矩阵。基于精确的参数矩阵，乘积矩阵的所有特征值都能以较高的相对精度计算出来。提供的数值实验证实了所宣称的高相对精度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Computing eigenvalues for products of two classes of sign regular matrices to high relative accuracy

In this paper, we consider how to accurately solve the product eigenvalue problem for the class of sign regular (SR) matrices with signature

(1, \dots, 1, - 1)

and the class of totally nonnegative (TN) matrices, which tend to be extremely ill-conditioned. We present algorithms with

O (n^{3})

complexity to accurately compute the parameter matrices of products of TN matrices and SR matrices with signature

(1, \dots, 1, - 1)

. Based on the accurate parameter matrices, all eigenvalues of the product matrix are computed to high relative accuracy. Numerical experiments are provided to confirm the claimed high relative accuracy.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.