Algorithm 795: PHCpack: A general-purpose solver for polynomial systems by homotopy continuation. Polynomial systems occur in a wide variety of application domains. Homotopy continuation methods are reliable and powerful methods to compute numerically approximations to all isolated complex solutions. During the last decade considerable progress has been accomplished on exploiting structure in a polynomial system, in particular its sparsity. In this paper the structure and design of the software package PHC is described. The main program operates in several modes, is menu-driven and file-oriented. This package features a great variety of root-counting methods among its tools. The outline of one black-box solver is sketched and a report is given on its performance on a large database of test problems. The software has been developed on four different machine architectures. Its portability is ensured by the gnu-ada compiler. (Source:

References in zbMATH (referenced in 221 articles , 1 standard article )

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  1. Hochstenbach, Michiel E.; van der Vorst, Henk A.: Alternatives to the Rayleigh quotient for the quadratic eigenvalue problem (2003)
  2. Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W.: Numerical irreducible decomposition (2003)
  3. Haas, Bertrand: A simple counterexample to Kouchnirenko’s conjecture (2002)
  4. Schreiber, H.; Meer, K.; Schmitt, B. J.: Dimensional synthesis of planar Stephenson mechanisms for motion generation using circlepoint search and homotopy methods (2002)
  5. Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W.: A method for tracking singular paths with application to the numerical irreducible decomposition (2002)
  6. Sturmfels, Bernd: Solving systems of polynomial equations (2002)
  7. Takeda, Akiko; Kojima, Masakazu; Fujisawa, Katsuki: Enumeration of all solutions of a combinatorial linear inequality system arising from the polyhedral homotopy continuation method (2002)
  8. Theobald, Thorsten: An enumerative geometry framework for algorithmic line problems in (\mathbbR^3) (2002)
  9. Ceberio, Martine; Granvilliers, Laurent: Solving nonlinear systems by constraint inversion and interval arithmetic (2001)
  10. Georg, Kurt: Improving the efficiency of exclusion algorithms (2001)
  11. Granvilliers, Laurent: On the combination of interval constraint solvers (2001)
  12. Li, T. Y.; Li, Xing: Finding mixed cells in the mixed volume computation (2001)
  13. Maekawa, Masahide; Noro, Masayuki; Takayama, Nobuki; Tamura, Yasushi; Ohara, Katsuyoshi: The design and implementation of OpenXM-RFC 100 and 101 (2001)
  14. Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W.: Numerical decomposition of the solution sets of polynomial systems into irreducible components (2001)
  15. Gao, Tangan; Li, T. Y.: Mixed volume computation via linear programming (2000)
  16. Huber, Birkett; Verschelde, Jan: Pieri homotopies for problems in enumerative geometry applied to pole placement in linear systems control (2000)
  17. Sommese, Andrew J.; Verschelde, Jan: Numerical homotopies to compute generic points on positive dimensional algebraic sets (2000)
  18. Sottile, Frank: Real Schubert calculus: polynomial systems and a conjecture of Shapiro and Shapiro (2000)
  19. Verschelde, Jan: Toric Newton method for polynomial homotopies (2000)
  20. Wise, Steven M.; Sommese, Andrew J.; Watson, Layne T.: Algorithm 801: POLSYS_PLP. A partitioned linear product homotopy code for solving polynomial systems of equations. (2000)

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