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 41 articles , 1 standard article )

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  1. Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew: BertiniLab: a MATLAB interface for solving systems of polynomial equations (2016)
  2. Chen, Liping; Han, Lixing; Zhou, Liangmin: Computing tensor eigenvalues via homotopy methods (2016)
  3. Hauenstein, Jonathan D.; Liddell, Alan C.: Certified predictor-corrector tracking for Newton homotopies (2016)
  4. Jiao, Libin; Dong, Bo; Zhang, Jintao; Yu, Bo: Polynomial homotopy method for the sparse interpolation problem. I: Equally spaced sampling (2016)
  5. Rusu, David; Santoprete, Manuele: Bifurcations of central configurations in the four-body problem with some equal masses (2016)
  6. Chen, Tianran; Li, Tien-Yien: Homotopy continuation method for solving systems of nonlinear and polynomial equations (2015)
  7. Feng, Yong; Wu, Wenyuan; Zhang, Jingzhong; Chen, Jingwei: Exact bivariate polynomial factorization over $\mathbb Q$ by approximation of roots (2015)
  8. Führ, Hartmut; Rzeszotnik, Ziemowit: On biunimodular vectors for unitary matrices (2015)
  9. Li, Zhe; Sang, Haifeng: Verified error bounds for singular solutions of nonlinear systems (2015)
  10. Bates, Daniel J.; Davis, Brent; Eklund, David; Hanson, Eric; Peterson, Chris: Perturbed homotopies for finding all isolated solutions of polynomial systems (2014)
  11. Bates, Daniel J.; Niemerg, Matthew: Using monodromy to avoid high precision in homotopy continuation (2014)
  12. Chen, Tianran; Li, Tien-Yien; Wang, Xiaoshen: Theoretical aspects of mixed volume computation via mixed subdivision (2014)
  13. Chrysikos, Ioannis; Sakane, Yusuke: The classification of homogeneous Einstein metrics on flag manifolds with $b_2(M) = 1$ (2014)
  14. Luo, Zhongxuan; Feng, Erbao; Zhang, Jiejin: A numerical realization of the conditions of Max Nöther’s residual intersection theorem (2014)
  15. Adrovic, Danko; Verschelde, Jan: Polyhedral methods for space curves exploiting symmetry applied to the cyclic $n$-roots problem (2013)
  16. Beltrán, Carlos; Leykin, Anton: Robust certified numerical homotopy tracking (2013)
  17. Besana, Gian Mario; Di Rocco, Sandra; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W.: Cell decomposition of almost smooth real algebraic surfaces (2013)
  18. Hauenstein, Jonathan; He, Yang-Hui; Mehta, Dhagash: Numerical elimination and moduli space of vacua (2013)
  19. He, Yang-Hui; Mehta, Dhagash; Niemerg, Matthew; Rummel, Markus; Valeanu, Alexandru: Exploring the potential energy landscape over a large parameter-space (2013)
  20. 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)

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