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 63 articles , 1 standard article )

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  1. Chen, Tianran: Unmixing the mixed volume computation (2019)
  2. Leykin, Anton; Yu, Josephine: Beyond polyhedral homotopies (2019)
  3. Chen, Tianran: libtropicon: a scalable library for computing intersection points of generic tropical hyper-surfaces (2018)
  4. Mahmoud, Abdrhaman; Yu, Bo; Zhang, Xuping: Eigenfunction expansion method for multiple solutions of fourth-order ordinary differential equations with cubic polynomial nonlinearity (2018)
  5. Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew E.: Decoupling highly structured polynomial systems (2017)
  6. Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien: Mixed cell computation in HOM4ps (2017)
  7. Chen, Tianran; Mehta, Dhagash: Parallel degree computation for binomial systems (2017)
  8. Hauenstein, Jonathan D. (ed.); Sommese, Andrew J. (ed.): Foreword. What is numerical algebraic geometry? (2017)
  9. Hauenstein, Jonathan D.; Wampler, Charles W.: Unification and extension of intersection algorithms in numerical algebraic geometry (2017)
  10. Imbach, Rémi; Moroz, Guillaume; Pouget, Marc: A certified numerical algorithm for the topology of resultant and discriminant curves (2017)
  11. Wang, Yu; Wu, Wenyuan; Xia, Bican: A special homotopy continuation method for a class of polynomial systems (2017)
  12. Zhang, Xuping; Zhang, Jintao; Yu, Bo: Symmetric homotopy method for discretized elliptic equations with cubic and quintic nonlinearities (2017)
  13. Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew: BertiniLab: a MATLAB interface for solving systems of polynomial equations (2016)
  14. Chen, Liping; Han, Lixing; Zhou, Liangmin: Computing tensor eigenvalues via homotopy methods (2016)
  15. Hauenstein, Jonathan D.; Liddell, Alan C.: Certified predictor-corrector tracking for Newton homotopies (2016)
  16. Huang, Lihua; Li, Bin; Wang, Yuefang: Computation analysis of buckling loads of thin-walled members with open sections (2016)
  17. Jiao, Libin; Dong, Bo; Zhang, Jintao; Yu, Bo: Polynomial homotopy method for the sparse interpolation problem. I: Equally spaced sampling (2016)
  18. Rusu, David; Santoprete, Manuele: Bifurcations of central configurations in the four-body problem with some equal masses (2016)
  19. Timothy Duff, Cvetelina Hill, Anders Jensen, Kisun Lee, Anton Leykin, Jeff Sommars: Solving polynomial systems via homotopy continuation and monodromy (2016) arXiv
  20. Chen, Tianran; Li, Tien-Yien: Homotopy continuation method for solving systems of nonlinear and polynomial equations (2015)

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