PHCpack

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: http://dl.acm.org/)


References in zbMATH (referenced in 203 articles , 1 standard article )

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  1. Helmer, Martin: A direct algorithm to compute the topological Euler characteristic and Chern-Schwartz-MacPherson class of projective complete intersection varieties (2017)
  2. Malajovich, Gregorio: Computing mixed volume and all mixed cells in quermassintegral time (2017)
  3. Meng, F.; Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.: A stable and accurate partitioned algorithm for conjugate heat transfer (2017)
  4. Plestenjak, Bor: Minimal determinantal representations of bivariate polynomials (2017)
  5. Sturmfels, Bernd: Fitness, apprenticeship, and polynomials (2017)
  6. Wang, Yu; Wu, Wenyuan; Xia, Bican: A special homotopy continuation method for a class of polynomial systems (2017)
  7. Wu, Wenyuan; Zeng, Zhonggang: The numerical factorization of polynomials (2017)
  8. Zhang, Xuping; Zhang, Jintao; Yu, Bo: Symmetric homotopy method for discretized elliptic equations with cubic and quintic nonlinearities (2017)
  9. Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew: BertiniLab: a MATLAB interface for solving systems of polynomial equations (2016)
  10. Bliss, Nathan; Verschelde, Jan: Computing all space curve solutions of polynomial systems by polyhedral methods (2016)
  11. Chen, Liping; Han, Lixing; Zhou, Liangmin: Computing tensor eigenvalues via homotopy methods (2016)
  12. De Loera, Jesús A.; Petrović, Sonja; Stasi, Despina: Random sampling in computational algebra: Helly numbers and violator spaces (2016)
  13. Gross, Elizabeth; Harrington, Heather A.; Rosen, Zvi; Sturmfels, Bernd: Algebraic systems biology: a case study for the Wnt pathway (2016)
  14. Hauenstein, Jonathan D.; Liddell, Alan C.: Certified predictor-corrector tracking for Newton homotopies (2016)
  15. Helmer, Martin: Algorithms to compute the topological Euler characteristic, Chern-Schwartz-MacPherson class and Segre class of projective varieties (2016)
  16. Jensen, Anders; Leykin, Anton; Yu, Josephine: Computing tropical curves via homotopy continuation (2016)
  17. Jiao, Libin; Dong, Bo; Zhang, Jintao; Yu, Bo: Polynomial homotopy method for the sparse interpolation problem. I: Equally spaced sampling (2016)
  18. Leykin, Anton: Polynomial homotopy continuation in Macaulay2 (2016)
  19. Martín del Campo, Abraham; Sottile, Frank: Experimentation in the Schubert calculus (2016)
  20. Plestenjak, Bor; Hochstenbach, Michiel E.: Roots of bivariate polynomial systems via determinantal representations (2016)

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