On convergence of two-stage iterative scheme

被引：2

作者：

Shekhar, Vaibhav ^{[1
]}

Giri, Chinmay Kumar ^{[2
]}

Mishra, Debasisha ^{[1
]}

机构：

[1] Natl Inst Technol Raipur, Dept Math, Raipur, Madhya Pradesh, India

[2] Seemanta Engn Coll, Dept Math, Jharpokharia 757086, Odisha, India

来源：

JOURNAL OF ANALYSIS | 2021年 / 29卷 / 04期

关键词：

Linear system; Moore-Penrose inverse; nonnegativity; Proper splitting; Two-stage iterative method; Comparison theorem; REGULAR SPLITTINGS;

D O I：

10.1007/s41478-021-00306-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Climent and Perea [Journal of Computational and Applied Mathematics 58:43-48, 2003; MR2013603] proposed first the convergence theory of two-stage iterative scheme for solving real rectangular linear systems. In this article, we revisit the same theory. The first main result provides some sufficient conditions which guarantee that the induced splitting from a two-stage iterative scheme is a proper weak regular splitting. We then establish a few comparison results. Out of these, many are even new in nonsingular matrix setting. Further, we study the monotone convergence theory of the two-stage iterative method. Besides these, we also prove the uniqueness of a proper splitting of a rectangular matrix under certain assumptions.

引用

页码：1207 / 1226

页数：20

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