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 183 articles , 1 standard article )

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  1. Améndola, Carlos; Bliss, Nathan; Burke, Isaac; Gibbons, Courtney R.; Helmer, Martin; Hoşten, Serkan; Nash, Evan D.; Rodriguez, Jose Israel; Smolkin, Daniel: The maximum likelihood degree of toric varieties (2019-2019)
  2. Chen, Tianran: Unmixing the mixed volume computation (2019)
  3. Kosta, Dimitra; Kubjas, Kaie: Maximum likelihood estimation of symmetric group-based models via numerical algebraic geometry (2019)
  4. Leykin, Anton; Yu, Josephine: Beyond polyhedral homotopies (2019)
  5. 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)
  6. Breiding, Paul; Timme, Sascha: HomotopyContinuation.jl: a package for homotopy continuation in Julia (2018)
  7. Charles, Zachary; Boston, Nigel: Exploiting algebraic structure in global optimization and the Belgian chocolate problem (2018)
  8. Leykin, Anton: Homotopy continuation in Macaulay2 (2018)
  9. Mahmoud, Abdrhaman; Yu, Bo; Zhang, Xuping: Eigenfunction expansion method for multiple solutions of fourth-order ordinary differential equations with cubic polynomial nonlinearity (2018)
  10. Telen, Simon; Mourrain, Bernard; Barel, Marc Van: Solving polynomial systems via truncated normal forms (2018)
  11. Telen, Simon; Van Barel, Marc: A stabilized normal form algorithm for generic systems of polynomial equations (2018)
  12. Verschelde, Jan: A blackbox polynomial system solver on parallel shared memory computers (2018)
  13. Anders Jensen, Jeff Sommars, Jan Verschelde: Computing Tropical Prevarieties in Parallel (2017) arXiv
  14. Baharev, Ali; Domes, Ferenc; Neumaier, Arnold: A robust approach for finding all well-separated solutions of sparse systems of nonlinear equations (2017)
  15. Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew E.: Decoupling highly structured polynomial systems (2017)
  16. Bernardi, Alessandra; Daleo, Noah S.; Hauenstein, Jonathan D.; Mourrain, Bernard: Tensor decomposition and homotopy continuation (2017)
  17. Boralevi, Ada; van Doornmalen, Jasper; Draisma, Jan; Hochstenbach, Michiel E.; Plestenjak, Bor: Uniform determinantal representations (2017)
  18. Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien: Mixed cell computation in HOM4ps (2017)
  19. Cifuentes, Diego; Parrilo, Pablo A.: Sampling algebraic varieties for sum of squares programs (2017)
  20. Compagnoni, Marco; Notari, Roberto; Antonacci, Fabio; Sarti, Augusto: On the statistical model of source localization based on range difference measurements (2017)

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