Proper Weak Regular Splitting and its Application to Convergence of\n Alternating Iterations

2016/02/05 by Debasisha Mishra, Mishra, Debasisha
Computer Science · Mathematics · #15A09 #Advanced Optimization Algorithms Research #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1602.01972

openalex publication_date 2016/02/05 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

The theory of matrix splitting is a useful tool for finding solution of\nrectangular linear system of equations, iteratively. The purpose of this paper\nis two-fold. Firstly, we revisit theory of weak regular splittings for\nrectangular matrices. Secondly, we propose an alternating iterative method for\nsolving rectangular linear systems by using the Moore-Penrose inverse and\ndiscuss its convergence theory, by extending the work of Benzi and Szyld\nNumererische Mathematik 76 (1997) 309-321; MR1452511]. Furthermore, a\ncomparison result is obtained which insures faster convergence rate of the\nproposed alternating iterative scheme.\n

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