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HOM4PS

swMATH ID: 410
Software Authors: Lee, T.L.; Li, T.Y.; Tsai, C.H.
Description: 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.
Homepage: http://www.math.nsysu.edu.tw/~leetsung/works/HOM4PS_soft.htm
Related Software: PHCpack; Bertini; PHoM; alphaCertified; Macaulay2; MixedVol; NumericalAlgebraicGeometry; SINGULAR; NAG4M2; DEMiCs; Hom4PS-3; HOMPACK90; PoSSo; STRINGVACUA; CoCoA; Paramotopy; HomotopyContinuation; Matlab; ISOLATE; Gfan
Referenced in: 81 Publications
all top 5

Referenced by 127 Authors

8 Hauenstein, Jonathan D.
7 Bates, Daniel J.
7 Chen, Tianran
6 Lee, Tsung-Lin
6 Li, Tien-Yien
6 Wu, Wenyuan
5 Mehta, Dhagash
5 Sommese, Andrew John
4 Leykin, Anton
4 Luo, Zhongxuan
4 Niemerg, Matthew E.
4 Wampler, Charles W. II
4 Yu, Bo
3 Beltrán, Carlos
3 Chen, Changbo
3 Dayar, Tugrul
3 Di Rocco, Sandra
3 Eklund, David
3 Feng, Erbao
3 Feng, Yong
3 He, Yang-Hui Evariste
3 Imbach, Rémi
3 Peterson, Chris
2 Dong, Bo
2 Gross, Elizabeth
2 Hill, Cvetelina
2 Hu, Wenyu
2 Newell, Andrew J.
2 Pouget, Marc
2 Santoprete, Manuele
2 Sottile, Frank
2 Staub, Florian
2 Su, Hai-Jun
2 Tari, Hafez
2 Verschelde, Jan
2 Zhang, JinTao
2 Zhang, Xuping
1 Adrovic, Danko
1 Alaeddini, Adel
1 Awange, Joseph L.
1 Besana, Gian Mario
1 Bozóki, Sándor
1 Breiding, Paul
1 Camargo-Molina, José Eliel
1 Castañeda-Sheissa, Roberto
1 Chen, Jingwei
1 Chen, Liping
1 Chrysikos, Ioannis
1 Davis, Brent R.
1 Decker, Wolfram
1 Duff, Timothy
1 Filobello-Nino, Uriel A.
1 Frohmader, Andrew
1 Führ, Hartmut
1 Han, Lixing
1 Hao, Wenrui
1 Heaton, Alexander
1 Hermanns, Holger
1 Huang, Lihua
1 Jensen, Anders Nedergaard
1 Jiao, Libin
1 Jimenez-Fernandez, Victor Manuel
1 Khan, Yasir
1 Kim, Sunyoung
1 Kojima, Masakazu
1 Lee, Kisun
1 Li, Zhe
1 Liddell, Alan C. jun.
1 Lin, Song-Sun
1 Lin, Wen-Wei
1 Luo, Xinlong
1 Lv, Jiahui
1 Mahmoud, Abdrhaman
1 Marigliano, Orlando
1 Marin-Hernandez, A.
1 Mathis, Pascal
1 Mevissen, Martin
1 Morais, António P.
1 Moroz, Guillaume
1 Oeding, Luke
1 Orhan, M. Can
1 Paláncz, Béla
1 Pardo, Luis Miguel
1 Pasechnik, Roman
1 Pfister, Gerhard
1 Reid, Greg J.
1 Rodriguez, Jose Israel
1 Rónyai, Lajos
1 Rüffer, Björn Sebastian
1 Rummel, Markus
1 Rusu, David
1 Rzeszotnik, Ziemowit
1 Sabeti, Rostam
1 Sakane, Yusuke
1 Sang, Haifeng
1 Schreck, Pascal
1 Schreyer, Frank-Olaf
1 Sheen, Dongwoo
1 Shirinkam, Sara
1 Sommars, Jeff
...and 27 more Authors
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Referenced in 44 Serials

8 Journal of Symbolic Computation
5 Applied Mathematics and Computation
5 Numerical Algorithms
4 Journal of High Energy Physics
4 Communications in Information and Systems
3 Foundations of Computational Mathematics
2 Mathematics of Computation
2 Journal of Scientific Computing
2 Mechanism and Machine Theory
2 Journal of Systems Science and Complexity
2 SIAM Journal on Applied Dynamical Systems
2 Journal of Algebra and its Applications
2 Mathematics in Computer Science
2 Advances in High Energy Physics
1 Computer Physics Communications
1 IMA Journal of Numerical Analysis
1 Computing
1 Journal of Applied Probability
1 Journal of Computational and Applied Mathematics
1 Numerische Mathematik
1 SIAM Journal on Numerical Analysis
1 Theoretical Computer Science
1 Advances in Applied Mathematics
1 Computer Aided Geometric Design
1 Discrete & Computational Geometry
1 Applied Mathematics Letters
1 SIAM Journal on Matrix Analysis and Applications
1 Computational Geometry
1 Journal of Global Optimization
1 Linear Algebra and its Applications
1 Mathematical Programming. Series A. Series B
1 Celestial Mechanics and Dynamical Astronomy
1 Experimental Mathematics
1 SIAM Journal on Scientific Computing
1 Applied Mathematics. Series B (English Edition)
1 Numerical Linear Algebra with Applications
1 ETNA. Electronic Transactions on Numerical Analysis
1 Bulletin des Sciences Mathématiques
1 Mathematical Problems in Engineering
1 Discrete Dynamics in Nature and Society
1 LMS Journal of Computation and Mathematics
1 Advances in Geometry
1 SpringerBriefs in Mathematics
1 SIAM Journal on Mathematics of Data Science

Referencing Publications by Year