Additional Results on Convergence of Alternating Iterations Involving Rectangular Matrices. (1st February 2017)

• Record Type: Journal Article
• Authors: Giri, Chinmay Kumar; Mishra, Debasisha
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 2(2017)
• Page Start: 160
• Page End: 180
• Publication Date: 2017-02-01
• Subjects: Comparison theorem -- convergence theorem -- iterative methods -- linear systems -- Moore–Penrose inverse -- non-negativity -- proper splitting; 15A09; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1232732
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: Different classes of matrix splittings of semi-monotone matrices lead to many comparison results, which are useful tools in examining the convergence rate of iterative methods for solving rectangular systems of linear equations in a faster way. In this context, the theory of alternating iterations for rectangular matrices was introduced recently, in order to arrive at the desired solution of accuracy or at the exact solution. In this article, we expand convergence theory of such alternating iterations and obtain comparison results for such iterations.