Accelerating Krawczyk-like interval algorithms for the solution of nonlinear systems of equations by using second derivatives

Recently the properties of Krawczyk-like iterative interval methods for the solution of systems of nonlinear equations have been discussed in several papers (e.g. 2], 3], 5], 6]). These methods converge to a solution under relatively weak conditions provided an initial inclusion vector is known. In the present paper we describe a method that improves the convergence speed for an important class of problems by using second partial derivatives. This method is particularly interesting for large systems with a Jacobi matrix whose off-diagonal coefficients are all constant.