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 168 articles , 1 standard article )

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  1. Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.: High-order upwind schemes for the wave equation on overlapping grids: Maxwell’s equations in second-order form (2018)
  2. Mahmoud, Abdrhaman; Yu, Bo; Zhang, Xuping: Eigenfunction expansion method for multiple solutions of fourth-order ordinary differential equations with cubic polynomial nonlinearity (2018)
  3. Telen, Simon; Van Barel, Marc: A stabilized normal form algorithm for generic systems of polynomial equations (2018)
  4. Anders Jensen, Jeff Sommars, Jan Verschelde: Computing Tropical Prevarieties in Parallel (2017) arXiv
  5. Baharev, Ali; Domes, Ferenc; Neumaier, Arnold: A robust approach for finding all well-separated solutions of sparse systems of nonlinear equations (2017)
  6. Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew E.: Decoupling highly structured polynomial systems (2017)
  7. Bernardi, Alessandra; Daleo, Noah S.; Hauenstein, Jonathan D.; Mourrain, Bernard: Tensor decomposition and homotopy continuation (2017)
  8. Boralevi, Ada; van Doornmalen, Jasper; Draisma, Jan; Hochstenbach, Michiel E.; Plestenjak, Bor: Uniform determinantal representations (2017)
  9. Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien: Mixed cell computation in HOM4ps (2017)
  10. Cifuentes, Diego; Parrilo, Pablo A.: Sampling algebraic varieties for sum of squares programs (2017)
  11. Compagnoni, Marco; Notari, Roberto; Antonacci, Fabio; Sarti, Augusto: On the statistical model of source localization based on range difference measurements (2017)
  12. David Kahle, Christopher O’Neill, Jeff Sommars: A computer algebra system for R: Macaulay2 and the m2r package (2017) arXiv
  13. Hauenstein, Jonathan D. (ed.); Sommese, Andrew J. (ed.): Foreword. What is numerical algebraic geometry? (2017)
  14. Helmer, Martin: A direct algorithm to compute the topological Euler characteristic and Chern-Schwartz-MacPherson class of projective complete intersection varieties (2017)
  15. Malajovich, Gregorio: Computing mixed volume and all mixed cells in quermassintegral time (2017)
  16. Meng, F.; Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.: A stable and accurate partitioned algorithm for conjugate heat transfer (2017)
  17. Plestenjak, Bor: Minimal determinantal representations of bivariate polynomials (2017)
  18. Sturmfels, Bernd: Fitness, apprenticeship, and polynomials (2017)
  19. Wu, Wenyuan; Zeng, Zhonggang: The numerical factorization of polynomials (2017)
  20. Zhang, Xuping; Zhang, Jintao; Yu, Bo: Symmetric homotopy method for discretized elliptic equations with cubic and quintic nonlinearities (2017)

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