About geometrical convergence of general iterative methods applied to nonunique solvable convex problems, Part II

Abstract

In Part I of this paper (in the preceeding issue) general conditions were given in a Hilbert space setting, ensuring the geometrical convergence of a sequence ( x k ) to a fixed element x . of a convex and closed subset M. Furthermore, corresponding error estimates were presented and some applications to the approximate solution of convex problems with a solution set M were indicated. In this part the mentioned applications are investigated in more detail. We use the iterative scheme x k + 1 = T k ( x k − λ k t k ) to get elements in M, where the occurring operators T k , elements t k and parameters λ k fulfil certain relations depending on M.