Iterative Methods for Fixed Point Problems in Hilbert Spaces - Cegielski, Andrzej; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013)
Iterative methods for finding fixed points of non-expansive operators in Hilbert spaces have been described in many publications. In this monograph we try to present the methods in a consolidated way. We introduce several classes of operators, examine their properties, define iterative methods generated by operators from these classes and present general convergence theorems. On this basis we discuss the conditions under which particular methods converge. A large part of the results presented in this monograph can be found in various forms in the literature (although several results presented here are new). We have tried, however, to show that the convergence of a large class of iteration methods follows from general properties of some classes of operators and from some general convergence theorems.
1 Introduction -- 2 Algorithmic Operators -- 3 Convergence of Iterative Methods -- 4 Algorithmic Projection Operators -- 5 Projection methods.
Keywords: Mathematics; Functional analysis; Operator theory; Numerical analysis; Mathematical optimization; Mathematics; Optimization; Functional Analysis; Calculus of Variations and Optimal Control; Optimization; Numerical Analysis; Operator Theory