Computing eigenvalues of quasi-rational Bernstein-Vandermonde matrices to high relative accuracy

被引：9

作者：

Yang, Zhao ^{[1
,3
]}

Ma, Xiao-Xiao ^{[2
,3
]}

机构：

[1] Shaanxi Univ Technol, Sch Math & Comp Sci, Hanzhong 723001, Shaanxi, Peoples R China

[2] Hunan Univ, Sch Math, Changsha, Peoples R China

[3] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan, Peoples R China

来源：

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 2022年 / 29卷 / 03期

关键词：

eigenvalues; generalized sign regular matrices; high relative accuracy; parameter matrix; quasi-rational Bernstein-Vandermonde matrix; SINGULAR-VALUES; COMPUTATIONS; SYSTEMS; FACTORIZATIONS; DECOMPOSITION; ALGORITHM;

D O I：

10.1002/nla.2421

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider how to accurately solve the eigenvalue problem for a class of quasi-rational Bernstein-Vandermonde (q-RBV) matrices. This class of matrices belongs to generalized sign regular matrices with signature (1, horizontal ellipsis ,1,-1). An algorithm is developed to accurately compute the parameter matrix for q-RBV matrices. Based on the parameter matrix, all the eigenvalues of q-RBV matrices have been computed to high relative accuracy. The perturbation theory for the eigenvalues of q-RBV matrices and the error analysis of our proposed algorithm are provided. Numerical experiments are performed to confirm the claimed high relative accuracy.

引用

页数：21

共 43 条

[1]

Alfa AS, 2002, MATH COMPUT, V71, P217, DOI 10.1090/S0025-5718-01-01325-4

[2] TOTALLY POSITIVE MATRICES [J].