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

References in zbMATH (referenced in 47 articles , 1 standard article )

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  1. Luo, Xin-long; Xiao, Hang; Lv, Jia-hui: Continuation Newton methods with the residual trust-region time-stepping scheme for nonlinear equations (2022)
  2. Luo, Xin-long; Xiao, Hang: Generalized continuation Newton methods and the trust-region updating strategy for the underdetermined system (2021)
  3. Easterling, David R.; Watson, Layne T.; Ramakrishnan, Naren: Probability-one homotopy methods for constrained clustering (2018)
  4. Chupin, Maxime; Haberkorn, Thomas; Trélat, Emmanuel: Low-thrust Lyapunov to Lyapunov and halo to halo missions with (L^2)-minimization (2017)
  5. Luo, Zhongxuan; Feng, Erbao; Zhang, Jiejin: A numerical realization of the conditions of Max Nöther’s residual intersection theorem (2014)
  6. Torres-Muñoz, D.; Vazquez-Leal, H.; Hernandez-Martinez, L.; Sarmiento-Reyes, A.: Improved spherical continuation algorithm with application to the double-bounded homotopy (DBH) (2014)
  7. Hao, Wenrui; Hauenstein, Jonathan D.; Shu, Chi-Wang; Sommese, Andrew J.; Xu, Zhiliang; Zhang, Yong-Tao: A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws (2013)
  8. Caillau, J.-B.; Cots, O.; Gergaud, J.: Differential continuation for regular optimal control problems (2012)
  9. Trélat, E.: Optimal control and applications to aerospace: some results and challenges (2012)
  10. Di Rocco, Sandra; Eklund, David; Peterson, Chris; Sommese, Andrew J.: Chern numbers of smooth varieties via homotopy continuation and intersection theory (2011)
  11. Fan, Xiaona; Yan, Qinglun: Homotopy method for solving ball-constrained variational inequalities (2011)
  12. Wampler, Charles W.; Sommese, Andrew J.: Numerical algebraic geometry and algebraic kinematics (2011)
  13. Borkovsky, Ron N.; Doraszelski, Ulrich; Kryukov, Yaroslav: A user’s guide to solving dynamic stochastic games using the homotopy method (2010)
  14. Di Rocco, Sandra; Eklund, David; Sommese, Andrew J.; Wampler, Charles W.: Algebraic (\mathbbC^*)-actions and the inverse kinematics of a general 6R manipulator (2010)
  15. Tari, Hafez; Su, Hai-Jun; Li, Tien-Yien: A constrained homotopy technique for excluding unwanted solutions from polynomial equations arising in kinematics problems (2010)
  16. Ahuja, Kapil; Watson, Layne T.; Billups, Stephen C.: Probability-one homotopy maps for mixed complementarity problems (2008)
  17. Chen, Yong; An, Hongli: Homotopy perturbation method for a type of nonlinear coupled equations with parameters derivative (2008)
  18. Kojima, Masakazu: Efficient evaluation of polynomials and their partial derivatives in homotopy continuation methods (2008)
  19. Thacker, W. I.; Wang, C. Y.; Watson, L. T.: Effect of flexible joints on the stability and large deflections of a triangular frame (2008)
  20. Ascher, U. M.; Huang, H.; van den Doel, K.: Artificial time integration (2007)

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