Technische Universität Berlin, Fachbereich 3 (Mathematik), D-1000, Berlin 12, Fed. Rep. Germany
Abstract:
We describe a vectorized algorithm for an interval arithmetic Newton-like method for a class of systems of nonlinear equations arising from discretizations of nonlinear elliptic PDE. This method converges to a solution under relatively weak conditions. It is founded on a combination of a Newton-like interval method and interval arithmetic ‘fast’ direct solver. In the present paper we focus our attention on aspects of the vectorization, in particular that of a simulation of an interval arithmetic and that of the direct solver.