HOMPACK

Systems of nonlinear equations, polynomial systems

The algorithms in HOMPACK are based on probability-one homotopy maps and are globally convergent with probability one under mild assumptions. There are three qualitatively different algorithms (ODE based, normal flow, augmented Jacobian matrix) for tracking the homotopy zero curve, and also different codes for dense and sparse problems. The code is modular and arranged hierarchically, so the user can call a driver supplying very little information or can call the tracking routines directly with complete control.

HOMPACK includes special algorithms for finding all solutions to a polynomial system, with a simple tableau input format for the polynomial coefficients. The routines are self-documenting, and several test programs are included.

The code is written in double precision ANSI Fortran 77. There is also a Fortran 90 version available from the author. Machine dependencies are restricted to the subroutine D1MACH. The software can be obtained from Netlib (send index from hompack)

Need more info?

Contact:

Layne T. Watson 
Department of Computer Science 
Virginia Polytechnic Institute & State University 
Blacksburg, VA 24061-0106 
Phone: (540) 231-7540 
ltw@vtopus.cs.vt.edu 

Visit Layne T. Watson's homepage, or the HOMPACK homepage

Reference:

A. P. Morgan, A. J. Sommese, and L. T. Watson, Finding all isolated solutions to polynomial systems using HOMPACK, ACM Trans. Math. Software 15 (1989), pp. 93--122.

L. T. Watson, Numerical linear algebra aspects of globally convergent homotopy methods, SIAM Rev. 28 (1986), pp. 529--545.

L. T. Watson, S. C. Billups, and A. P. Morgan, Algorithm 652: HOMPACK: A suite of codes for globally convergent homotopy algorithms, ACM Trans. Math. Software 13 (1987), pp. 281--310.

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