Further results on iterative methods for computing generalized inverses

Xiaoji Liu, Chumei Hu, Yaoming Yu

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10 Citations (Scopus)


In this paper, we reconsider the iterative method X-k = Xk-1 + beta Y (I - AX(k-1)), k = 1, 2, ..., beta is an element of C \ 0 for computing the generalized inverse A(T,S)((2)) 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).
Original languageEnglish
Pages (from-to)684 - 694
Number of pages11
JournalJournal of Computational and Applied Mathematics
Issue number3
Publication statusPublished - 2010

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