HOMPACK90: A Suite of FORTRAN 90 Codes for Globally Convergent Homotopy Algorithms

Abstract

HOMPACK90 is a FORTRAN 90 version of the FORTRAN 77 package HOMPACK (Algorithm 652), a collection of codes for finding zeros or fixed points of nonlinear systems using globally convergent probability-one homotopy algorithms. Three qualitatively different algorithms - ordinary differential equation based, normal flow, quasi-Newton augmented Jacobian matrix - are provided for tracking homotopy zero curves, as well as separate routines for dense and sparse Jacobian matrices. A high level driver for the special case of polynomial systems is also provided. Changes to HOMPACK include numerous minor improvements, simpler and more elegant interfaces, use of modules, new end games, support for several sparse matrix data structures, and new iterative algorithms for large sparse Jacobian matrices.