Lt. Watson et al., ALGORITHM-777 - HOMPACK90 - A SUITE OF FORTRAN-90 CODES FOR GLOBALLY CONVERGENT HOMOTOPY ALGORITHMS, ACM transactions on mathematical software, 23(4), 1997, pp. 514-549
HOMPACK90 is a Fortran 90 version of the Fortran 77 package HOMPACK (A
lgorithm 652), a collection of codes for finding zeros or fixed points
of nonlinear systems using globally convergent probability-one homoto
py algorithms. Three qualitatively different algorithms-ordinary diffe
rential equation based, normal flow, quasi-Newton augmented Jacobian m
atrix-are provided for tracking homotopy zero curves, as well as separ
ate routines for dense and sparse Jacobian matrices. A high level driv
er for the special case of polynomial systems is also provided. Change
s to HOMPACK include numerous minor improvements, simpler and more ele
gant interfaces, use of modules, new end games, support for several sp
arse matrix data structures, and new iterative algorithms for large sp
arse Jacobian matrices.