Iterative methods for computing generalized inverses

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. 2000 Mathematics subject classification: primary 46H05, 47A05, 90C30, 15A09. Keywords and phrases: generalized inverses, Moore-Penrose inverse, iterative methods, nonlinear optimization.

• Type: Journal
• Year: 2007
• Where: AMC
• Authors: Dragan S. Djordjevic
• Keywords: AMC 2007, C∗ -algebras, Iterative Methods, Order Optimization Methods