HOMPACK90 swMATH ID: 412 Software Authors: Watson, Layne T.; Sosonkina, Maria; Melville, Robert C.; Morgan, Alexnder P.;Walker, Homer F. Description: HOMPACK90 is a Fortran 90 version of the Fortran 77 package HOMPACK by L. T. Watson, S. C. Billups and A. P. Morgan [ibid. 13, No. 3, 281-310 (1987; Zbl 0626.65049)], a collection of codes for finding zeros or fixed points of nonlinear systems using globally convergent probability-one homotopy algorithms. Three qualitatively different algorithms – ordinary differential equation based, normal flow, quasi-Newton augmented Jacobian matrix – are provided for tracking homotopy zero curves, as well as separate routines for dense and sparse Jacobian matrices. A high level driver for the special case of polynomial systems is also provided. Changes to HOMPACK include numerious minor improvements, simpler and more elegant interfaces, use of modules, new end games, support for several sparse matrix data structures, and new iterative algorithms for large sparse Jacobian matrices Homepage: http://people.cs.vt.edu/~ltw/hompack/hompack90.html Related Software: HOMPACK; PHCpack; POLSYS_PLP; HOM4PS; Bertini; PHoM; LAPACK; Matlab; POLSYS_GLP; minpack; RODAS; BVPh; bvp4c; NewtonLib; ADIFOR; MINOS; PITCON; NACLab; fsolve.m; Regularization tools Cited in: 46 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Algorithm 777: HOMPACK90: A suite of Fortran 90 codes for globally convergent homotopy algorithms. Zbl 0913.65042Watson, Layne T.; Sosonkina, Maria; Melville, Robert C.; Morgan, Alexnder P.; Walker, Homer F. 1997 all top 5 Cited by 92 Authors 10 Watson, Layne Terry 6 Sommese, Andrew John 3 Kojima, Masakazu 3 Wampler, Charles W. II 2 Di Rocco, Sandra 2 Donev, Aleksandar 2 Eklund, David 2 Gergaud, Joseph 2 Haberkorn, Thomas 2 Kim, Sunyoung 2 Luo, Xinlong 2 Martínez, José Mario 2 Ramakrishnan, Naren 2 Stillinger, Frank H. jun. 2 Su, Hai-Jun 2 Torquato, Salvatore 2 Trélat, Emmanuel 2 Verschelde, Jan 2 Xiao, Hang 1 Ahuja, Kapil 1 An, Hongli 1 Ascher, Uri M. 1 Bae, Kyung 1 Billups, Stephen C. 1 Birgin, Ernesto G. 1 Borkovsky, Ron N. 1 Caillau, Jean-Baptiste 1 Chang, Shing-Lin 1 Chen, Yong 1 Chien, Cheng-Sheng 1 Chupin, Maxime 1 Cots, Olivier 1 Dai, Yang 1 Dang, Chuangyin 1 Dent, Deborah 1 Dieci, Luca 1 Doraszelski, Ulrich 1 Easterling, David R. 1 Fan, Xiaona 1 Feng, Erbao 1 Feng, Guochen 1 Gasparo, Maria Grazia 1 Gürdal, Zafer 1 Hao, Wenrui 1 Hauenstein, Jonathan D. 1 He, Jian 1 Hernandez-Martínez, Luis 1 Huang, Hui 1 Jiang, Jing 1 Jonsson, Gudbjorn F. 1 Krejić, Nataša 1 Kryukov, Yaroslav 1 Kucaba-Pietal, Anna 1 Laudański, Ludomir M. 1 Li, Tien-Yien 1 Luo, Zhongxuan 1 Lv, Jiahui 1 McCarthy, J. Michael 1 Mei, Zhen 1 Melville, Robert C. 1 Morgan, Alexander P. 1 O’Leary, Dianne P. 1 Papini, Alessandra 1 Paprzycki, Marcin 1 Peterson, Chris 1 Ragon, S. A. 1 Rheinboldt, Werner C. 1 Riaza, Ricardo 1 Sarmiento-Reyes, Arturo 1 Shaffer, Clifford A. 1 Shu, Chi-Wang 1 Sosonkina, Maria 1 Sosonkina, Masha 1 Tari, Hafez 1 Thacker, William I. 1 Torres-Muñoz, Delia 1 Tranter, William H. 1 Tyson, John J. 1 Vavasis, Stephen A. 1 Vázquez-Leal, Héctor 1 Verstak, Alex 1 Walker, Homer F. 1 Wang, Chang-Yi 1 Wise, Steven M. 1 Xu, Qing 1 Xu, Zhiliang 1 Yan, Qinglun 1 Yu, Bo 1 Zhang, Jiejin 1 Zhang, Yongtao 1 Zufiria, Pedro J. 1 Zwolak, Jason W. all top 5 Cited in 25 Serials 7 Journal of Computational and Applied Mathematics 4 Applied Mathematics and Computation 3 Journal of Computational Physics 3 ACM Transactions on Mathematical Software 2 Journal of Symbolic Computation 2 Computational Optimization and Applications 2 Optimization Methods & Software 1 Acta Mechanica 1 International Journal of Solids and Structures 1 Mathematics of Computation 1 BIT 1 Journal of the Operations Research Society of Japan 1 Journal of Optimization Theory and Applications 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Operations Research 1 Journal of Scientific Computing 1 Numerical Algorithms 1 International Journal of Computer Mathematics 1 Applied Mathematics. Series B (English Edition) 1 Computational and Applied Mathematics 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Mechanism and Machine Theory 1 Nonlinear Analysis. Real World Applications 1 Acta Numerica 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis all top 5 Cited in 23 Fields 33 Numerical analysis (65-XX) 9 Operations research, mathematical programming (90-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 5 Algebraic geometry (14-XX) 5 Mechanics of particles and systems (70-XX) 4 Mechanics of deformable solids (74-XX) 3 Commutative algebra (13-XX) 3 Ordinary differential equations (34-XX) 3 Computer science (68-XX) 2 Field theory and polynomials (12-XX) 2 Real functions (26-XX) 2 Functions of a complex variable (30-XX) 2 Partial differential equations (35-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 History and biography (01-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Statistics (62-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Citations by Year