Multiplicative algorithms for determining positive solutions of nonlinear equations

Abstract

New schemes for developing iterative algorithms based on a special nonlinear (multiplicative) transformation are proposed. These schemes are applied to computing positive solutions of nonlinear equations. Modifications of multiplicative algorithms which use parallel and coordinatewise scheme of iterations are considered. Convergence theorems are proved. Multiplicative algorithms are used for solving some problems of urban planning, transportation research, and image reconstruction which can be described by the problem of entropy maximization. Results of computation experiments are included.