NONLINEAR SYSTEMS OF EQUATIONS

WE PROPOSE TO BUILD A STATE-OF-THE-ART SOFTWARE PACKAGE FOR SOLVING GENERAL LARGE SYSTEMS OF NONLINEAR EQUATIONS. ALTHOUGH THERE ARE SEVERAL SOFTWARE PACKAGES FOR SOLVING LARGE SPARSE LINEAR SYSTEMS (SPARSEPACK, YSMP, HAREWELL, FOR EXAMPLE), SIMILAR PACKAGES FOR NONLINEAR SYSTEMS ARE ALMOST NONEXISTENT. WE PROPOSE TO CONSTRUCT A COLLECTION OF ROUTINES INCORPORATING WELL-ESTABLISHED VARIATIONS OF NEWTON'S METHOD AND THE LATEST RESEARCH DEVELOPMENTS IN NONLINEAR SYSTEMS SOLUTION. IN PARTICULAR, OUR PACKAGE WILL EMPLOY JACOBIANFREE METHODS. THESE ARE ESPECIALLY APPEALING BECAUSE OF THEIR FLEXIBILITY AND LOW MEMORY REQUIREMENTS. THE PACKAGE WILL BE EASY TO USE AND EFFICIENT.