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 203 articles , 1 standard article )

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  1. Aghassi, Michele; Bertsimas, Dimitris: Robust game theory (2006)
  2. Buot, Max-Louis G.; Richards, Donald St. P.: Counting and locating the solutions of polynomial systems of maximum likelihood equations. I. (2006)
  3. Gunji, T.; Kim, S.; Fujisawa, K.; Kojima, M.: PHoMpara-parallel implementation of the polyhedral homotopy continuation method for polynomial systems (2006)
  4. Iglesias, Andrés (ed.); Takayama, Nobuki (ed.): Mathematical software -- ICMS 2006. Second international congress on mathematical software, Castro Urdiales, Spain, September 1--3, 2006. Proceedings (2006)
  5. Leykin, Anton; Verschelde, Jan: Interfacing with the numerical homotopy algorithms in PHCpack (2006)
  6. Leykin, Anton; Verschelde, Jan; Zhao, Ailing: Newton’s method with deflation for isolated singularities of polynomial systems (2006)
  7. Leykin, Anton; Verschelde, Jan; Zhuang, Yan: Parallel homotopy algorithms to solve polynomial systems (2006)
  8. Su, Hai-Jun; Mccarthy, J. Michael; Sosonkina, Masha; Watson, Layne T.: Algorithm 857: POLSYS(_-)GLP -- a parallel general linear product homotopy code for solving polynomial systems of equations. (2006)
  9. Wu, Wenyuan; Reid, Greg: Application of numerical algebraic geometry and numerical linear algebra to PDE (2006)
  10. Gao, Tangan; Li, T. Y.; Wu, Mengnien: Algorithm 846: MixedVol: a software package for mixed-volume computation. (2005)
  11. Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W.: An intrinsic homotopy for intersecting algebraic varieties (2005)
  12. Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W.: Introduction to numerical algebraic geometry (2005)
  13. Syam, Muhammed I.: Nonlinear optimization exclusion tests for finding all solutions of nonlinear equations (2005)
  14. Kim, S.; Kojima, M.: Numerical stability of path tracing in polyhedral homotopy continuation methods (2004)
  15. Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W.: Homotopies for intersecting solution components of polynomial systems (2004)
  16. Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W.: Numerical factorization of multivariate complex polynomials (2004)
  17. Syam, Muhammed I.: Finding all real zeros of polynomial systems using multi-resultant (2004)
  18. Datta, Ruchira S.: Using computer algebra to find Nash equilibria (2003)
  19. Gao, Tangan; Li, T. Y.: Mixed volume computation for semi-mixed systems (2003)
  20. Georg, Kurt: A new exclusion test. (2003)

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