On convergence of two-stage iterative scheme On convergence of two-stage iterative scheme

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...

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Bibliographic Details
Published in:The Journal of Analysis Vol. 29; no. 4; pp. 1207 - 1226
Main Authors: Shekhar, Vaibhav, Giri, Chinmay Kumar, Mishra, Debasisha
Format: Journal Article
Language:English
Published: Singapore Springer Singapore 01.12.2021
Subjects:
Abstract Harmonic Analysis
Analysis
Fourier Analysis
Functional Analysis
Mathematics
Mathematics and Statistics
Measure and Integration
Original Research Paper
Special Functions
Linear system
Moore–Penrose inverse
Proper splitting
nonnegativity
Two-stage iterative method
Comparison theorem
15A09
ISSN:0971-3611, 2367-2501
Online Access:Get full text
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Summary: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.
Bibliography:Communicated by Samy Ponnusamy.
ISSN:0971-3611
2367-2501
DOI:10.1007/s41478-021-00306-9