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Zbl 0981.47001
Djordjević, Dragan S.; Stanimirović, Predrag S.
Splittings of operators and generalized inverses. (English)
[J] Publ. Math. 59, No.1-2, 147-159 (2001). ISSN 0033-3883

Summary: We extend the notion of the proper splitting of rectangular matrices introduced and investigated in {\it Berman, A.} and {\it Neumann, M.} [SIAM J. Appl. Math. 31, 307-312 (1976; Zbl 0352.65017)] and {\it Berman, A.} and {\it Plemmons, R. J.} [SIAM J. Numer. Anal. 11, 145-154 (1974; Zbl 0273.65029)] to $g$-invertible operators on Banach spaces. Also, we extend and generalize the notion of the index splitting of square matrices introduced and investigated in {\it Wei, Y.} [Appl. Math. Comput. 95, 115-124 (1998; Zbl 0942.15003)] introducing the $\{T,S\}$-splitting for arbitrary operators on Banach spaces. The index splitting is a partial case of $\{T,S\}$-splitting. The obtained results extend and generalize various well-known results for square and rectangular complex matrices.

MSC 2000:: *47A05 General theory of linear operators
15A09 Matrix inversion
47A50 Equations and inequalities involving linear operators
65F20 Overdetermined systems (numerical linear algebra)
65J10 Equations with linear operators (numerical methods)

Keywords: generalized inverses; splittings of operators; iterative methods

Citations: Zbl 0352.65017; Zbl 0273.65029; Zbl 0942.15003

Cited in: Zbl 1111.15007

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