Accurate bidiagonal decompositions of Cauchy–Vandermonde matrices of any rank

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2024-08-07 DOI:10.1002/nla.2579

Jorge Delgado, Plamen Koev, Ana Marco, José‐Javier Martínez, Juan Manuel Peña, Per‐Olof Persson, Steven Spasov

引用次数: 0

Abstract

We present a new decomposition of a Cauchy–Vandermonde matrix as a product of bidiagonal matrices which, unlike its existing bidiagonal decompositions, is now valid for a matrix of any rank. The new decompositions are insusceptible to the phenomenon known as subtractive cancellation in floating point arithmetic and are thus computable to high relative accuracy. In turn, other accurate matrix computations are also possible with these matrices, such as eigenvalue computation amongst others.

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任意秩 Cauchy-Vandermonde 矩阵的精确对角分解

我们将考奇-万德蒙德矩阵分解为对角矩阵的乘积，与现有的对角分解不同，这种新分解现在对任意秩的矩阵都有效。新的分解不受浮点运算中的减法抵消现象的影响，因此可计算出较高的相对精度。反过来，利用这些矩阵还可以进行其他精确的矩阵计算，如特征值计算等。

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

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.