HOM4PS
HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method. HOM4PS-2.0 is a software package in FORTRAN 90 which implements the polyhedral homotopy continuation method for solving polynomial systems. It updates its original version HOM4PS in three key aspects: (1) a new method for finding mixed cells; (2) combining the polyhedral and linear homotopies in one step; (3) a new way of dealing with curve jumping. Numerical results show that this revision leads to a spectacular speed-up, ranging up to 1950s, over its original version on all benchmark systems, especially for large ones. It surpasses the existing packages in finding isolated zeros, such as PHCpack [J. Verschelde, ACM Trans. Math. Softw. 25, No. 2, 251–276 (1999; Zbl 0961.65047)] PHoM [T. Gunji et al., Computing 73, No. 1, 57–77 (2004; Zbl 1061.65041)] and Bertini [D. J. Bates et al., in: Stillman, Michael E. (ed.) et al., Software for algebraic geometry. Papers of a workshop, Minneapolis, MN, USA, October 23–27, 2006. New York, NY: Springer. The IMA Volumes in Mathematics and its Applications 148, 1–14 (2008; Zbl 1143.65344), available at http://www.nd.edu/ sommese/bertini], in speed by big margins.
Keywords for this software
References in zbMATH (referenced in 65 articles , 1 standard article )
Showing results 61 to 65 of 65.
Sorted by year (- Anton Leykin: Numerical Algebraic Geometry for Macaulay2 (2009) arXiv
- Lee, Tsung-Lin; Santoprete, Manuele: Central configurations of the five-body problem with equal masses (2009)
- Leykin, Anton; Sottile, Frank: Galois groups of Schubert problems via homotopy computation (2009)
- Mevissen, Martin; Yokoyama, Kosuke; Takayama, Nobuki: Solutions of polynomial systems derived from the steady cavity flow problem (extended abstract). (2009)
- Lee, T. L.; Li, T. Y.; Tsai, C. H.: HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method (2008)