Further results on iterative methods for computing generalized inverses

Authors:
Xiaoji Liu;Chunmei Hu;Yaoming Yu
Affiliations:
College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, PR China;College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, PR China;School of Mathematical Sciences, Building 28, Monash University, VIC 3800, Australia
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 4
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Abstract

In this paper, we reconsider the iterative method X"k=X"k"-"1+@bY(I-AX"k"-"1), k=1,2,...,@b@?C@?{0} for computing the generalized inverse A"T","S^(^2^) over Banach spaces or the generalized Drazin inverse a^d of a Banach algebra element a, reveal the intrinsic relationship between the convergence of such iterations and the existence of A"T","S^(^2^) or a^d, and present the error bounds of the iterative methods for approximating A"T","S^(^2^) or a^d. Moreover, we deduce some necessary and sufficient conditions for iterative convergence to A"T","S^(^2^) or a^d.