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Iterative methods for computing generalized inverses related with optimization methods

Published online by Cambridge University Press:  09 April 2009

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 ‖x2 by means of the known second order unconstrained minimization methods. We give several examples which illustrate our theory.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2005

References

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