Consistent approximations in Newton-type decomposition methods

Summary A class of Newton-type decomposition methods for the solution of large systems of nonlinear equations recently introduced by the first two authors is extended in such a way that consistent approximations to the derivatives by appropriate difference quotients are permitted. Concrete realizations with essential merits for practical computation and a rigorous convergence analysis are given. For special choices of the discretization parameterR-orders greater than one are derived.Dedicated to Prof. Dr. Dr. h.c. Lothar Collatz on the occasion of his 75th birthday