Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms

Authors:
Layne T. Watson;Stephen C. Billups;Alexander P. Morgan
Affiliations:
Departments of Electrical Engineering and Computer Science, Industrial and Operations Engineering and Mathematics, University of Michigan, Ann Arbor, MI and Virginia Polytechnic Institute and Stat ...;Safety Assessment Technologies Division 7233, Sandia National Laboratories, Albuquerque, NM;Mathematics Department, General Motors Research Laboratories, Warren, MI
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
1987

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Abstract

There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK provides three qualitatively different algorithms for tracking the homotopy zero curve: ordinary differential equation-based, normal flow, and augmented Jacobian matrix. Separate routines are also provided for dense and sparse Jacobian matrices. A high-level driver is included for the special case of polynomial systems.