The strength of nonstationary iteration

Abstract

This is the second of three papers in which we study global convergence of iterations using linear information for the solution of nonlinear equations. In Wasilkowski [6] we proved that for the class of all analytic scalar complex functions having only simple zeros there exists no globally convergentstationary iteration using linear information. Here we exhibit anonstationary iteration using linear information which is globally convergent even for the multivariate and abstract cases. This demonstrates the strength of nonstationary iteration. In Wasilkowski [7] we shall prove that any globally convergent iteration using linear information hasinfinite complexity even for the class of scalar complex polynomials having only simple zeros.