Monday, May 28, 2012

Integration in first-order arithmetic

Jan has finished an implementation of a primitive function operation on first-order polynomials with interval coefficients. This is one of the main components of the Picard operators that are the basis for the hybrid interval ODE solver that is under development. The main difficulty was in the choice of degree reduction algorithm, which maps the nonlinear terms generated buy integration back to first-order form. The next component Jan will target is the containment relation, which is used to detect when iterated application of the Picard operator may be terminated.