PHoMpara swMATH ID: 1928 Software Authors: Gunji, T.; Kim, S.; Fujisawa, K.; Kojima, M. Description: PHoMpara-parallel implementation of the polyhedral homotopy continuation method for polynomial systems. The polyhedral homotopy continuation method (PHoM) is known to be a successful method for finding all isolated solutions of a system of polynomial equations. PHoM, an implementation of the method in C++, finds all isolated solutions of a polynomial system by constructing a family of modified polyhedral homotopy functions, tracing the solution curves of the homotopy equations, and verifying the obtained solutions. A software package PHoMpara parallelizes PHoM to solve a polynomial system of large size. Many characteristics of the polyhedral homotopy continuation method make parallel implementation efficient and provide excellent scalability. Numerical results include some large polynomial systems that had not been solved. Homepage: http://link.springer.com/article/10.1007%2Fs00607-006-0166-2 Keywords: polynomials; parallel computation; numerical experiments; software package; polyhedral homotopy continuation method; numerical results Related Software: PHCpack; PHoM; POLSYS_PLP; POLSYS_GLP; MonodromySolver; Macaulay2; DEMiCs; Bertini; Database of Polynomial Systems; PoSSo; Ninf-G/MPI Cited in: 5 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year PHoMpara-parallel implementation of the polyhedral homotopy continuation method for polynomial systems. Zbl 1122.65048Gunji, T.; Kim, S.; Fujisawa, K.; Kojima, M. 2006 all top 5 Cited by 16 Authors 2 Leykin, Anton 1 Bates, Daniel J. 1 Bliss, Nathan 1 Duff, Timothy 1 Fujisawa, Katsuki 1 Gunji, Takayuki 1 Hauenstein, Jonathan D. 1 Kim, Sunyoung 1 Kojima, Masakazu 1 Mizutani, Tomohiko 1 Sommars, Jeff 1 Sommese, Andrew John 1 Takeda, Akiko 1 Verschelde, Jan 1 Wampler, Charles W. II 1 Zhuang, Yan Cited in 1 Serial 1 Computing all top 5 Cited in 6 Fields 4 Numerical analysis (65-XX) 3 Algebraic geometry (14-XX) 2 Field theory and polynomials (12-XX) 2 Functions of a complex variable (30-XX) 2 Computer science (68-XX) 1 Real functions (26-XX) Citations by Year