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/)
Keywords for this software
References in zbMATH (referenced in 203 articles , 1 standard article )
Showing results 21 to 40 of 203.
Sorted by year (- Breiding, Paul; Timme, Sascha: HomotopyContinuation.jl: a package for homotopy continuation in Julia (2018)
- Charles, Zachary; Boston, Nigel: Exploiting algebraic structure in global optimization and the Belgian chocolate problem (2018)
- Kang, Weirui; Zeng, Jiani; Liu, Qinghua; Huang, Zhengdong: Generating the isocurve representation for configuration space of mechanisms (2018)
- Leykin, Anton: Homotopy continuation in Macaulay2 (2018)
- Mahmoud, Abdrhaman; Yu, Bo; Zhang, Xuping: Eigenfunction expansion method for multiple solutions of fourth-order ordinary differential equations with cubic polynomial nonlinearity (2018)
- Telen, Simon; Mourrain, Bernard; Barel, Marc Van: Solving polynomial systems via truncated normal forms (2018)
- Telen, Simon; Van Barel, Marc: A stabilized normal form algorithm for generic systems of polynomial equations (2018)
- Verschelde, Jan: A blackbox polynomial system solver on parallel shared memory computers (2018)
- Anders Jensen, Jeff Sommars, Jan Verschelde: Computing Tropical Prevarieties in Parallel (2017) arXiv
- Baharev, Ali; Domes, Ferenc; Neumaier, Arnold: A robust approach for finding all well-separated solutions of sparse systems of nonlinear equations (2017)
- Batenkov, Dmitry: Accurate solution of near-colliding Prony systems via decimation and homotopy continuation (2017)
- Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew E.: Decoupling highly structured polynomial systems (2017)
- Bernardi, Alessandra; Daleo, Noah S.; Hauenstein, Jonathan D.; Mourrain, Bernard: Tensor decomposition and homotopy continuation (2017)
- Boralevi, Ada; van Doornmalen, Jasper; Draisma, Jan; Hochstenbach, Michiel E.; Plestenjak, Bor: Uniform determinantal representations (2017)
- Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien: Mixed cell computation in HOM4ps (2017)
- Cifuentes, Diego; Parrilo, Pablo A.: Sampling algebraic varieties for sum of squares programs (2017)
- Compagnoni, Marco; Notari, Roberto; Antonacci, Fabio; Sarti, Augusto: On the statistical model of source localization based on range difference measurements (2017)
- David Kahle, Christopher O’Neill, Jeff Sommars: A computer algebra system for R: Macaulay2 and the m2r package (2017) arXiv
- Hauenstein, Jonathan D. (ed.); Sommese, Andrew J. (ed.): Foreword. What is numerical algebraic geometry? (2017)
- Hauenstein, Jonathan D.; Wampler, Charles W.: Unification and extension of intersection algorithms in numerical algebraic geometry (2017)