Accurate computation of the Moore-Penrose inverse of strictly totally positive matrices

被引：44

作者：

Marco, Ana ^{[1
]}

Martinez, Jose-Javier ^{[1
]}

机构：

[1] Univ Alcala, Dept Fis & Matemat, Madrid 28871, Spain

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 350卷

关键词：

Moore-Penrose inverse; Inverse; Totally positive matrix; Neville elimination; Bidiagonal decomposition; High relative accuracy; VANDERMONDE MATRICES; BIDIAGONAL DECOMPOSITION; ITERATIVE METHOD; ERROR ANALYSIS; FACTORIZATIONS;

D O I：

10.1016/j.cam.2018.10.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The computation of the Moore-Penrose inverse of structured strictly totally positive matrices is addressed. Since these matrices are usually very ill-conditioned, standard algorithms fail to provide accurate results. An algorithm based on the QR factorization and which takes advantage of the special structure and the totally positive character of these matrices is presented. The first stage of the algorithm consists of the accurate computation of the bidiagonal decomposition of the matrix. Numerical experiments illustrating the good behavior of our approach are included. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：299 / 308

页数：10

共 38 条

[1]

[Anonymous], 1997, NUMERICAL LINEAR ALG

[2]

Ben-Israel A., 2002, The Electronic Journal of Linear Algebra, V9, P150

[3]

Bjorck A., 2015, NUMERICAL METHODS MA, V59

[4]

Bjorck A, 1996, NUMERICAL METHODS LE, DOI DOI 10.1137/1.9781611971484