Generalized Information and Maximal Order of Iteration for Operator Equations

Abstract

We consider stationary iterative methods for the solution of operator equations which use “generalized information”. We seek methods with maximal order provided the points of iterations are in “good position”. The new concepts of order of information and “generalized” interpolatory methods are introduced. The main result states that the maximal order is equal to the order of information which depends on generalized information and on the position of iteration points. We show that the maximal order is achievable by the generalized interpolatory method.