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Iterative methods for computing generalized inverses related with optimization methods

Part of: Topological algebras, normed rings and algebras, Banach algebras Basic linear algebra General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Dragan S. Djordjević  and
Predrag S. Stanimirović
Dragan S. Djordjević
Affiliation:
Department of MathematicsUniversity of NišFaculty of Science and MathematicsP.O. Box 224 Višegradska 33 18000 Niš Serbia e-mail: dragan@pmf.ni.ac.yu, pecko@pmf.ni.ac.yu
Predrag S. Stanimirović
Affiliation:
Department of MathematicsUniversity of NišFaculty of Science and MathematicsP.O. Box 224 Višegradska 33 18000 Niš Serbia e-mail: dragan@pmf.ni.ac.yu, pecko@pmf.ni.ac.yu
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Abstract

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We develop several iterative methods for computing generalized inverses using both first and second order optimization methods in C*-algebras. Known steepest descent iterative methods are generalized in C*-algebras. We introduce second order methods based on the minimization of the norms ‖Ax − b‖2 and ‖x‖2 by means of the known second order unconstrained minimization methods. We give several examples which illustrate our theory.

Keywords

generalized inversesMoore-Penrose inverseiterative methodsnonlinearoptimization

MSC classification

Secondary: 46H05: General theory of topological algebras 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 90C30: Nonlinear programming 15A09: Matrix inversion, generalized inverses
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 78 , Issue 2 , April 2005 , pp. 257 - 272
Copyright
Copyright © Australian Mathematical Society 2005

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