Rigorous Verification for the Solution of Nonlinear Interval System

Abstract

We survey a general method for solving nonlinear interval systems of equations. In particular, we paid special attention to the computational aspects of linear interval systems since the bulk of computations are done during the stage of computing outer estimation of the including linear interval systems. The height of our findings is the synchronization of Hansen’s theorem with that due to Rohn to accelerate basic convergence characteristics of our method. We compare computed results with those obtained by Sainz et al where Kaucher interval arithmetic was applied on interval Jacobi iterative type method and found out that our proposed method gave quite impressive results.

Keywords: nonlinear interval systems of equations, interval newton method, Hansen’s method, Rohn’s method, kaucher arithmetic.