High relative accuracy with some special matrices related to Γ and β functions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-23 DOI:10.1002/nla.2494

J. Delgado, J. Peña

引用次数: 0

Abstract

For some families of totally positive matrices using Γ$$ \Gamma $$ and β$$ \beta $$ functions, we provide their bidiagonal factorization. Moreover, when these functions are defined over integers, we prove that the bidiagonal factorization can be computed with high relative accuracy and so we can compute with high relative accuracy their eigenvalues, singular values, inverses and the solutions of some associated linear systems. We provide numerical examples illustrating this high relative accuracy.

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与Γ和β函数有关的一些特殊矩阵的高相对精度

对于一些使用Γ$$\Gamma$$和β$$\beta$$函数的全正矩阵族，我们给出了它们的二重分解。此外，当这些函数定义在整数上时，我们证明了双对角因子分解可以以高相对精度计算，因此我们可以以高的相对精度计算它们的特征值、奇异值、逆和一些相关线性系统的解。我们提供了说明这种高相对精度的数值例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.