swMATH ID: 5324
Software Authors: Watson, Layne T.; Billups, Stephen C.; Morgan, Alexander P.
Description: Algorithm 652, HOMPACK: A suite of codes for globally convergent homotopy algorithms. There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK provides three qualitatively different algorithms for tracking the homotopy zero curve: ordinary differential equation-based, normal flow, and augmented Jacobian matrix. Separate routines are also provided for dense and sparse Jacobian matrices. A high-level driver is included for the special case of polynomial systems.
Homepage: http://netlib.org/cgi-bin/netlibfiles.pl?filename=/toms/652
Keywords: optimization; ZERO – Zeros of Functions and Systems
Related Software: PITCON; HOMPACK90; minpack; Matlab; PHCpack; Bertini; ALCON; PHoM; POLSYS_PLP; HOM4PS; AUTO; NAG4M2; Hom4PS-3; PoSSo; MINOS; NITSOL; NL2SOL; RODAS; DIMSIM; KELLEY
Cited in: 121 Publications
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Cited by 154 Authors

29 Watson, Layne Terry
11 Morgan, Alexander P.
10 Sommese, Andrew John
7 Yu, Bo
5 Herings, P. Jean-Jacques
5 Verschelde, Jan
4 Jackiewicz, Zdzislaw
4 Kostreva, Michael M.
4 Li, Tien-Yien
4 Martínez, José Mario
4 Peeters, Ronald
4 Schmedders, Karl H.
4 Thacker, William I.
4 Vázquez-Leal, Héctor
4 Wampler, Charles W. II
4 Wang, Chang-Yi
4 Zhu, Zhichuan
3 Billups, Stephen C.
3 Chien, Cheng-Sheng
3 Eaves, B. Curtis
3 Ribbens, Calvin J.
3 Stewart, David Edward
3 Walker, Homer F.
2 Allison, Donald C. S.
2 Bernstein, Dennis S.
2 Chang, Shing-Lin
2 Chen, Ke
2 Chen, Tianran
2 Collins, Emmanuel G. jun.
2 DeMarzo, Peter M.
2 Haegemans, Ann
2 Hernandez-Martínez, Luis
2 Irani, Kashmira M.
2 Kalaba, Robert E.
2 Kumar, S. Kishore
2 Lee, Tsung-Lin
2 Lin, Wen-Wei
2 Martin, Clyde Franklin
2 Mei, Zhen
2 Poore, Aubrey B.
2 Sauer, Timothy D.
2 Torres-Muñoz, Delia
2 Yang, Fenlin
2 Yang, Li
1 Albrecht, Gudrun
1 An, Hongli
1 Andò, Alessia
1 Andreani, Roberto
1 Anitescu, Mihai
1 Beck, James L.
1 Birgin, Ernesto G.
1 Bonilla, Julián
1 Bourji, Samih K.
1 Breda, Dimitri
1 Brown, Donald J.
1 Butcher, John C.
1 Cardone, Angelamaria
1 Castañeda-Sheissa, Roberto
1 Chang, Shu-Ming
1 Charpentier, Isabelle
1 Chen, Yong
1 Chu, Moody T.
1 Cools, Ronald
1 De Moor, Bart L. R.
1 Desa, Colin
1 Dickenstein, Alicia M.
1 Diehl, Moritz Mathias
1 Domes, Ferenc
1 Duintjer Tebbens, Jurjen
1 Easterling, David R.
1 Emiris, Ioannis Z.
1 Fan, Xiaona
1 Fang, Liang
1 Farouki, Rida T.
1 Filobello-Nino, Uriel A.
1 Friedlander, Ana
1 Ge, Yuzhen
1 Gürdal, Zafer
1 Gutman, Shaul
1 Guttalu, Ramesh S.
1 Hadian, J.
1 Haftka, Raphael T.
1 Hao, Wenrui
1 Harimoto, S.
1 Hartmann, Stefan
1 He, Guoping
1 Hirasawa, Kotaro
1 Hodel, A. Scottedward
1 Hu, Jinglu
1 Inoue, Yasuaki
1 Jimenez-Fernandez, Victor Manuel
1 Judd, Kenneth L.
1 Kapania, Rakesh K.
1 Keil, Frerich J.
1 Khan, Yasir
1 Kinard, L. A.
1 Kraus, František J.
1 Krejić, Nataša
1 Kubler, Felix
1 Kumamaru, Kousuke
...and 54 more Authors
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Cited in 60 Serials

13 Applied Mathematics and Computation
9 Journal of Computational and Applied Mathematics
6 Computers & Mathematics with Applications
4 ACM Transactions on Mathematical Software
4 Journal of Optimization Theory and Applications
3 Numerische Mathematik
3 SIAM Journal on Scientific and Statistical Computing
3 Journal of Economic Dynamics & Control
3 Computational and Applied Mathematics
3 Economic Theory
2 Acta Mechanica
2 International Journal of Solids and Structures
2 SIAM Journal on Numerical Analysis
2 Applied Numerical Mathematics
2 Journal of Symbolic Computation
2 Journal of Scientific Computing
2 Annals of Operations Research
2 Journal of Global Optimization
2 International Journal of Computer Mathematics
2 SIAM Journal on Optimization
2 Optimization Methods & Software
2 Nonlinear Analysis. Theory, Methods & Applications
1 Computer Methods in Applied Mechanics and Engineering
1 International Journal of Control
1 International Journal for Numerical Methods in Fluids
1 Journal of Computational Physics
1 The Arabian Journal for Science and Engineering
1 Automatica
1 International Journal of Game Theory
1 Journal of Economic Theory
1 Journal of Mathematical Economics
1 Mathematics of Operations Research
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Theoretical Computer Science
1 Optimal Control Applications & Methods
1 Advances in Applied Mathematics
1 Computer Science in Economics and Management
1 The Journal of Supercomputing
1 Numerical Algorithms
1 IEEE Transactions on Circuits and Systems. I: Fundamental Theory and Applications
1 Applied Mathematical Modelling
1 European Journal of Operational Research
1 Linear Algebra and its Applications
1 IEE Proceedings. Part D. Control Theory and Applications
1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
1 Computational Optimization and Applications
1 Numerical Linear Algebra with Applications
1 Advances in Computational Mathematics
1 Journal of Vibration and Control
1 Journal of Inequalities and Applications
1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
1 Optimization and Engineering
1 Mathematical Modelling and Analysis
1 Fixed Point Theory
1 International Journal of Numerical Analysis and Modeling
1 Journal of Industrial and Management Optimization
1 Algorithms and Computation in Mathematics
1 Discrete and Continuous Dynamical Systems. Series S
1 Numerical Algebra, Control and Optimization
1 International Journal of Applied and Computational Mathematics

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