Accurate computations with Lupa matrices

被引：15

作者：

Delgado, Jorge ^{[1
]}

Pena, J. M. ^{[2
]}

机构：

[1] Univ Zaragoza, Dept Matemat Aplicada, Teruel, Spain

[2] Univ Zaragoza, Dept Matemat Aplicada, Zaragoza, Spain

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2017年 / 303卷

关键词：

Accurate computations; Bidiagonal decompositions; Lupas operator; Totally positive matrices; Q-ANALOG; NEVILLE ELIMINATION; BERNSTEIN OPERATOR; TOTAL POSITIVITY;

D O I：

10.1016/j.amc.2017.01.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Lupas q-analogues of the Bernstein functions play an important role in Approximation Theory and Computer Aided Geometric Design. Their collocation matrices are called Lupas matrices. In this paper, we provide algorithms for computing the bidiagonal decomposition of these matrices and their inverses to high relative accuracy. It is also shown that these algorithms can be used to perform to high relative accuracy several algebraic calculations with these matrices, such as the calculation of their inverses, their eigenvalues or their singular values. Numerical experiments are included. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：171 / 177

页数：7

共 20 条

[1] TOTALLY POSITIVE MATRICES [J].