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Iterative methods for computing generalized inverses and splittings of operators. (English) Zbl 1160.65312

Author’s abstract: We consider an iterative method for computing generalized inverses of linear operators, based on splittings of operators. Thus, the result from Y. L. Chen and X. Y. Tan [Appl. Math. Comput. 163, No. 1, 309–325 (2005; Zbl 1069.65041)] is extended to infinite dimensional settings.

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
65F10 Iterative numerical methods for linear systems

Citations:

Zbl 1069.65041
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Full Text: DOI

References:

[1] Ben-Israel, A.; Grevile, T. N.E., Generalized Inverses: Theory and Applications (2003), Springer
[2] Berman, A.; Neumann, M., Proper splittings of rectangular matrices, SIAM J. Appl. Math., 31, 307312 (1976)
[3] Djordjević, D. S.; Stanimirović, P. S., New type of matrix splitting and its applications, Acta Math. Hungarica, 92, 1-2, 121-135 (2001) · Zbl 0994.15005
[4] Djordjević, D. S.; Stanimirović, P. S., Splitting of operators and generalized inverses, Publ. Math. Debrecen, 59, 147-159 (2001) · Zbl 0994.15005
[5] Djordjević, D. S.; Wei, Y., Outer generalized inverses in rings, Comm. Algebra, 33, 3051-3060 (2005) · Zbl 1111.15007
[6] Chen, Yong-Lin; Tan, Xue-Yuan, Computing generalized inverses of matrices by iterative methods based on splitting of matrices, Appl. Math. Comp., 163, 309-325 (2005) · Zbl 1069.65041
[7] Wei, Y.; Djordjević, D. S.; Stanimirović, P. S., The representation and approximation of outer generalized inverses, Acta Math. Hungarica, 104, 1-2, 1-26 (2004) · Zbl 1071.65075
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