The stability of formulae of the Gohberg-Semencul-Trench type for Moore-Penrose and group inverses of Toeplitz matrices

被引：13
作者：
Xie, Pengpeng [1 ]
Wei, Yimin [1 ,2 ]
机构：
[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
[2] Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2016年 / 498卷
基金：
中国国家自然科学基金;
关键词：
Toeplitz matrix; Moore-Penrose inverse; Group inverse; LSQR; DGMRES; DISPLACEMENT STRUCTURE; ALGORITHM; DGMRES;
D O I：
10.1016/j.laa.2015.01.029
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a stability analysis of Gohberg-Semencul-Trench type formulae for the Moore-Penrose and group inverses of singular Toeplitz matrices. We develop a fast algorithm for the computation of the Moore-Penrose inverse based on a Gohberg-Semencul-Trench type formula and the LSQR method. For the group inverse, the DGMRES method is used to perform the fast computation. Numerical tests show that the fast algorithms designed here are at least as good as the known Newton iteration. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：117 / 135
页数：19
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