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 198 articles , 1 standard article )
Showing results 1 to 20 of 198.
Sorted by year (- Bozorgmanesh, Hassan; Hajarian, Masoud: Solving tensor E-eigenvalue problem faster (2020)
- Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas: Identifying the parametric occurrence of multiple steady states for some biological networks (2020)
- Hao, Wenrui; Zheng, Chunyue: An adaptive homotopy method for computing bifurcations of nonlinear parametric systems (2020)
- Harris, Corey; Helmer, Martin: Segre class computation and practical applications (2020)
- Menini, Laura; Possieri, Corrado; Tornambè, Antonio: A symbolic algorithm to compute immersions of polynomial systems into linear ones up to an output injection (2020)
- Zhu, Lailai; Stone, Howard A.: Harnessing elasticity to generate self-oscillation via an electrohydrodynamic instability (2020)
- Adamer, Michael F.; Helmer, Martin: Complexity of model testing for dynamical systems with toric steady states (2019)
- 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)
- Chen, Justin; Kileel, Joe: Numerical implicitization: a Macaulay2 package (2019)
- Chen, Tianran: Unmixing the mixed volume computation (2019)
- Kosta, Dimitra; Kubjas, Kaie: Maximum likelihood estimation of symmetric group-based models via numerical algebraic geometry (2019)
- Leykin, Anton; Yu, Josephine: Beyond polyhedral homotopies (2019)
- Obatake, Nida; Shiu, Anne; Tang, Xiaoxian; Torres, Angélica: Oscillations and bistability in a model of ERK regulation (2019)
- 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)
- Bliss, Nathan; Verschelde, Jan: The method of Gauss-Newton to compute power series solutions of polynomial homotopies (2018)
- 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)