Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 224, Issue -, Pages 671-680Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2013.08.086
Keywords
Moore-Penrose; Singular matrix; Approximate inverse; GMRES method; Rectangular matrix; Preconditioning
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In this paper, an iterative scheme is proposed to find the roots of a nonlinear equation. It is shown that this iterative method has fourth order convergence in the neighborhood of the root. Based on this iterative scheme, we propose the main contribution of this paper as a new high-order computational algorithm for finding an approximate inverse of a square matrix. The analytical discussions show that this algorithm has fourth-order convergence as well. Next, the iterative method will be extended by theoretical analysis to find the pseudo-inverse (also known as the Moore-Penrose inverse) of a singular or rectangular matrix. Numerical examples are also made on some practical problems to reveal the efficiency of the new algorithm for computing a robust approximate inverse of a real (or complex) matrix. (C) 2013 Elsevier Inc. All rights reserved.
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