J. Aust. Math. Soc.  78 (2005), 257-272
Iterative methods for computing generalized inverses related with optimization methods

Dragan S. Djordjevic
  Department of Mathematics
  University of Nis
  Faculty of Science and Mathematics
  P.O. Box 224
  Visegradska 33
  18000 Nis
  Serbia
  dragan@pmf.ni.ac.yu
and
Predrag S. Stanimirovic
  Department of Mathematics
  University of Nis
  Faculty of Science and Mathematics
  P.O. Box 224
  Visegradska 33
  18000 Nis
  Serbia
  pecko@pmf.ni.ac.yu


Abstract
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.
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