Proper Weak Regular Splitting and its Application to Convergence of Alternating Iterations
For researchers in numerical linear algebra, this work extends existing theory to rectangular systems but is incremental, building on prior work by Benzi and Szyld.
This paper revisits weak regular splitting theory for rectangular matrices and proposes an alternating iterative method using the Moore-Penrose inverse for solving rectangular linear systems, with convergence analysis and a comparison result showing faster convergence.
The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular matrices. Secondly, we propose an alternating iterative method for solving rectangular linear systems by using the Moore-Penrose inverse and discuss its convergence theory, by extending the work of Benzi and Szyld Numererische Mathematik 76 (1997) 309-321; MR1452511]. Furthermore, a comparison result is obtained which insures faster convergence rate of the proposed alternating iterative scheme.