On decomposition of collocation matrices for the Cauchy–Bernstein basis and applications

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-11-24 DOI:10.1016/j.aml.2024.109391

Zhao Yang , Tao Chen , Sanyang Liu

引用次数: 0

Abstract

In this paper, we show that collocation matrices of the Cauchy–Bernstein basis can be decomposed as products of a Cauchy–Vandermonde matrix and a block diagonal matrix. A useful application of this result is that the explicit expression of the determinant for the collocation matrices is presented. Consequently, an algorithm is provided to accurately compute the determinants. Numerical experiments confirm the high accuracy of the algorithm.

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Cauchy-Bernstein基下配置矩阵的分解及其应用

本文证明了Cauchy-Bernstein基的搭配矩阵可以分解为Cauchy-Vandermonde矩阵和块对角矩阵的乘积。该结果的一个有用的应用是给出了配置矩阵行列式的显式表达式。因此，提供了一种精确计算行列式的算法。数值实验证明了该算法具有较高的精度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.