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Quotient convergence and multi-splitting methods for solving singular linear equations

Content Provider	Springer Nature Link
Author	Cui, Xiaoke Wei, Yimin Zhang, Naimin
Copyright Year	2007
Abstract	In this paper, we use the group inverse to characterize the quotient convergence of an iterative method for solving consistent singular linear systems, when the matrix index equals one. Next, we show that for stationary splitting iterative methods, the convergence and the quotient convergence are equivalent, which was first proved in [7]. Lastly, we propose a (multi-)splitting iterative method A=F–G, where the splitting matrix F may be singular, endowed with group inverse, by using F # as a solution tool for any iteration. In this direction, sufficient conditions for the quotient convergence of these methods are given. Then, by using the equivalence between convergence and quotient convergence, the classical convergence of these methods is proved. These latter results generalize Cao’s result, which was given for nonsingular splitting matrices F. Keywords: Group inverse, singular linear equations, iterative method, P-regular splitting, Hermitian positive definite matrix, multi-splitting, quotient convergence AMS Classification: 15A09, 65F35
Starting Page	21
Ending Page	31
Page Count	11
File Format	PDF
ISSN	00080624
Journal	CALCOLO
Volume Number	44
Issue Number	1
e-ISSN	11265434
Language	English
Publisher	Springer-Verlag
Publisher Date	2007-01-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Numerical Analysis Theory of Computation
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Computational Mathematics

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