Verification methods for nonlinear equations with saddle point functions

Abstract

This paper presents a fast verification algorithm for nonlinear equations with saddle point functions. This algorithm is based on a block decomposition of the Krawczyk-type interval operator, which can be applied to convex programming problems and nonlinear Navier–Stokes equations. We show the efficiency of this algorithm by comparing it with the Krawczyk method and the interval Newton-like method for the discretized stationary Navier–Stokes equations.