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.


References in zbMATH (referenced in 72 articles , 1 standard article )

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  1. Adrovic, Danko; Verschelde, Jan: Polyhedral methods for space curves exploiting symmetry applied to the cyclic (n)-roots problem (2013)
  2. Beltrán, Carlos; Leykin, Anton: Robust certified numerical homotopy tracking (2013)
  3. Besana, Gian Mario; Di Rocco, Sandra; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W.: Cell decomposition of almost smooth real algebraic surfaces (2013)
  4. Hauenstein, Jonathan; He, Yang-Hui; Mehta, Dhagash: Numerical elimination and moduli space of vacua (2013)
  5. He, Yang-Hui; Mehta, Dhagash; Niemerg, Matthew; Rummel, Markus; Valeanu, Alexandru: Exploring the potential energy landscape over a large parameter-space (2013)
  6. Vazquez-Leal, H.; Marin-Hernandez, A.; Khan, Y.; Yıldırım, A.; Filobello-Nino, U.; Castaneda-Sheissa, R.; Jimenez-Fernandez, V. M.: Exploring collision-free path planning by using homotopy continuation methods (2013)
  7. Wu, Wenyuan; Reid, Greg: Finding points on real solution components and applications to differential polynomial systems (2013)
  8. Chen, Tianran; Li, Tien-Yien: Spherical projective path tracking for homotopy continuation methods (2012)
  9. Dayar, Tuǧrul: Analyzing Markov chains using Kronecker products. Theory and applications (2012)
  10. Dayar, Tuğrul; Orhan, M. Can: Kronecker-based infinite level-dependent QBD processes (2012)
  11. Lee, Tsung-Lin; Lin, Song-Sun; Lin, Wen-Wei; Yau, Shing-Tung; Zhu, Ubo: Polynomial calculations in Doppler tracking (2012)
  12. Mehta, Dhagash; He, Yang-Hui; Hauenstein, Jonathan D.: Numerical algebraic geometry: a new perspective on gauge and string theories (2012)
  13. Bates, Daniel J.; Oeding, Luke: Toward a salmon conjecture (2011)
  14. Bates, Daniel J.; Sottile, Frank: Khovanskii-Rolle continuation for real solutions (2011)
  15. Beltrán, Carlos: A continuation method to solve polynomial systems and its complexity (2011)
  16. Beltrán, Carlos; Pardo, Luis Miguel: Fast linear homotopy to find approximate zeros of polynomial systems (2011)
  17. Dayar, T.; Hermanns, H.; Spieler, D.; Wolf, V.: Bounding the equilibrium distribution of Markov population models. (2011)
  18. Di Rocco, Sandra; Eklund, David; Peterson, Chris; Sommese, Andrew J.: Chern numbers of smooth varieties via homotopy continuation and intersection theory (2011)
  19. Luo, Zhongxuan; Hu, Wenyu; Feng, Erbao: Computing curve intersection by homotopy methods (2011)
  20. Luo, Zhongxuan; Hu, Wenyu; Sheen, Dongwoo: The nearest complex polynomial with a zero in a given complex domain (2011)