与Γ和β函数有关的一些特殊矩阵的高相对精度

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2023-01-23 DOI:10.1002/nla.2494

J. Delgado, J. Peña

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引用次数: 0

摘要

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。

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

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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来源期刊

Numerical Linear Algebra with Applications 数学-数学

CiteScore

3.40

自引率

2.30%

发文量

审稿时长

12 months

期刊介绍： Manuscripts submitted to Numerical Linear Algebra with Applications should include large-scale broad-interest applications in which challenging computational results are integral to the approach investigated and analysed. Manuscripts that, in the Editor’s view, do not satisfy these conditions will not be accepted for review. Numerical Linear Algebra with Applications receives submissions in areas that address developing, analysing and applying linear algebra algorithms for solving problems arising in multilinear (tensor) algebra, in statistics, such as Markov Chains, as well as in deterministic and stochastic modelling of large-scale networks, algorithm development, performance analysis or related computational aspects. Topics covered include: Standard and Generalized Conjugate Gradients, Multigrid and Other Iterative Methods; Preconditioning Methods; Direct Solution Methods; Numerical Methods for Eigenproblems; Newton-like Methods for Nonlinear Equations; Parallel and Vectorizable Algorithms in Numerical Linear Algebra; Application of Methods of Numerical Linear Algebra in Science, Engineering and Economics.