Iterative algorithms for constructing approximate solutions of nonlinear problems from erroneous inadequate data

Abstract

Two iterative algorithms for constructing approximate solutions of nonlinear problems from erroneous inadequate data are presented. These algorithms are basically hybrids of Newton's iterative methods and the inversion technique of Backus and Gilbert. Error estimates and criteria for truncation are given for the general situation, and for illustration a class of nonlinear integral equations of the first kind is used as an example.