Interval Algorithm For Solving System Of Nonlinear Equations

In the 1960s, America mathematician Moore carved out the subject of interval analysis which is one of important branches of numerical analysis and has so many aspects of applications, interval iteration method for solving system of nonlinear equa-tions is one of important applications for interval analysis. Every iteration of interval iteration method calculate errors of approximation solution and decide the existence of solution at the same time. Carefully analyze and study interval iteration method for solving system of nonlinear equations at this paper, based on this, then improve traditional interval iteration method, the main content of this paper is as follows:In chapter 1, research backgrounds and significance, research status of domestic and foreign, main content of this paper are introduced. Preliminary knowledge about basic conception of interval analysis, interval Newton method, interval Krawczyk iter-ation method and Magnitude algorithm are under discussion.In chapter 2, we put forward two multi-step interval iteration methods for solving system of nonlinear equations based on multi-step interval iteration methods for solv-ing nonlinear equation, then give the numerical judgment condition for existence of solution and verify the convergence on these iteration methods. At last, effectiveness of new proposed interval iteration methods is validated through numerical examples.In chapter 3, Magnitude algorithm for solving system of nonlinear equations is proposed combining Hansen-Sengupta iteration method and Magnitude algorithm for solving interval linear system, superiority of new proposed iteration algorithm has been verified compared with Hansen-Sengupta iteration method, effectiveness of Magnitude algorithm for solving system of nonlinear equations is validated further through numer-ical examples.In chapter 4, for system of nonlinear equations with interval parameter, we modify interval Krawczyk operator, then propose interval order-reduction method, based on above analysis, interval algorithm for obtain solution region of system of nonlinear equations with interval parameter has been build, and it is feasible for the algorithm by numerical examples.