Order Interval Test and Iterative Method for Nonlinear Systems

Abstract

An order interval test for existence and uniqueness of solutions to a nonlinear system is given. It combines the interval technique and the monotone iterative technique. It has the main merits of interval iterative methods but need not use interval arithmetic. An order interval Newton method is also given, which is globally convergent. It is a generalization of the results in [3,4,13.3].