A parameter perturbation technique applied to multipoint iteration functions for the solution of systems of nonlinear equations

The convergence of classical iterative procedures, when applied to a system of nonlinear algebraic or transcendental equations, is highly dependent upon a good initial approximation to the desired roots. Most of the classical iterative schemes have convergence factors between one and two. In this paper iterative schemes of order two and greater are studied in connection with a parameter perturbation process. The parameter perturbation process relaxes the restrictions on the choice of initial values. The procedure divides each problem into a number of subsidiary problems. Each subsidiary system of equations is then solved until a solution is found to the original problem. The study presents a discussion of the iteration functions chosen, of the parameter perturbation algorithm and the conditions for convergence --Abstract, page ii