Numerical Mathematics - NewtonLib. Software repository for Peter Deuflhards Book ”Newton Methods for Nonlinear Problems -- Affine Invariance and Adaptive Algorithms”. This monograph presents a scheme to construct adaptive Newton-type algorithms in close connection with an associated affine invariant convergence analysis. Part of these algorithms are presented as informal programs in the text. Some, but not all of the described algorithms have been worked out in detail. Below follows a list of codes mentioned by name in the book. All of the available programs (not only by the author and his group) are free as long as they are exclusively used for research or teaching purposes. For commercial use of the software you must sign a license-agreement with the ZIB and pay a license-charge that depends on the referenced software package and the intended usage. Please read our sample license agreement (or the german version) for more details.

References in zbMATH (referenced in 234 articles , 2 standard articles )

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  1. Zhang, Xiaolong; Boyd, John P.: Revisiting the Thomas-Fermi equation: accelerating rational Chebyshev series through coordinate transformations (2019)
  2. Deuflhard, Peter: The grand four: affine invariant globalizations of Newton’s method (2018)
  3. Jarlebring, E.; Koskela, A.; Mele, G.: Disguised and new quasi-Newton methods for nonlinear eigenvalue problems (2018)
  4. Magoulès, Frédéric; Gbikpi-Benissan, Guillaume; Zou, Qinmeng: Asynchronous iterations of parareal algorithm for option pricing models (2018)
  5. Mitsos, Alexander; Najman, Jaromił; Kevrekidis, Ioannis G.: Optimal deterministic algorithm generation (2018)
  6. Quirynen, Rien; Gros, Sébastien; Diehl, Moritz: Inexact Newton-type optimization with iterated sensitivities (2018)
  7. Chen, ChuanMiao; Hu, HongLing: Global existence of real roots and random Newton flow algorithm for nonlinear system of equations (2017)
  8. Grande, Jörg: Analysis of highly accurate finite element based algorithms for computing distances to level sets (2017)
  9. Hackbusch, Wolfgang; Kressner, Daniel; Uschmajew, André: Perturbation of higher-order singular values (2017)
  10. Karpinski, Stefan; Pop, Iuliu Sorin: Analysis of an interior penalty discontinuous Galerkin scheme for two phase flow in porous media with dynamic capillary effects (2017)
  11. Kungurtsev, Vyacheslav; Jäschke, Johannes: A predictor-corrector path-following algorithm for dual-degenerate parametric optimization problems (2017)
  12. Luan, Vu Thai: Fourth-order two-stage explicit exponential integrators for time-dependent PDEs (2017)
  13. Mehlmann, C.; Richter, T.: A finite element multigrid-framework to solve the sea ice momentum equation (2017)
  14. Potra, Florian A.: A superquadratic variant of Newton’s method (2017)
  15. Quirynen, Rien; Gros, Sébastien; Houska, Boris; Diehl, Moritz: Lifted collocation integrators for direct optimal control in ACADO toolkit (2017)
  16. Ramos, Higinio; Monteiro, M. T. T.: A new approach based on the Newton’s method to solve systems of nonlinear equations (2017)
  17. Shiryaev, Vladimir; Orlik, Julia: A one-dimensional computational model for hyperelastic string structures with Coulomb friction (2017)
  18. Toulopoulos, Ioannis; Wick, Thomas: Numerical methods for power-law diffusion problems (2017)
  19. Argyros, Ioannis K.; Hilout, Saïd: The majorant method in the theory of Newton-Kantorovich approximations and generalized Lipschitz conditions (2016)
  20. Auger, Anne; Hansen, Nikolaus: Linear convergence of comparison-based step-size adaptive randomized search via stability of Markov chains (2016)

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