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 245 articles , 2 standard articles )

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  1. Argyros, Ioannis K.; George, Santhosh: Kantorovich-like convergence theorems for Newton’s method using restricted convergence domains (2019)
  2. Gong, Shihua; Cai, Xiao-Chuan: A nonlinear elimination preconditioned inexact Newton method for heterogeneous hyperelasticity (2019)
  3. Hoppe, Ronald H. W.; Linsenmann, Christopher: (\mathrmC^0)-interior penalty discontinuous Galerkin approximation of a sixth-order Cahn-Hilliard equation modeling microemulsification processes (2019)
  4. Jarlebring, Elias: Broyden’s method for nonlinear eigenproblems (2019)
  5. Potschka, Andreas: Backward step control for Hilbert space problems (2019)
  6. Sun, Tianxiao; Quoc, Tran-Dinh: Generalized self-concordant functions: a recipe for Newton-type methods (2019)
  7. van der Vegt, J. J. W.; Xia, Yinhua; Xu, Yan: Positivity preserving limiters for time-implicit higher order accurate discontinuous Galerkin discretizations (2019)
  8. Zhang, Xiaolong; Boyd, John P.: Revisiting the Thomas-Fermi equation: accelerating rational Chebyshev series through coordinate transformations (2019)
  9. Deuflhard, Peter: The grand four: affine invariant globalizations of Newton’s method (2018)
  10. Jarlebring, E.; Koskela, A.; Mele, G.: Disguised and new quasi-Newton methods for nonlinear eigenvalue problems (2018)
  11. Jiang, Jiamin; Tchelepi, Hamdi A.: Dissipation-based continuation method for multiphase flow in heterogeneous porous media (2018)
  12. Kelley, C. T.: Numerical methods for nonlinear equations (2018)
  13. Magoulès, Frédéric; Gbikpi-Benissan, Guillaume; Zou, Qinmeng: Asynchronous iterations of parareal algorithm for option pricing models (2018)
  14. Mitsos, Alexander; Najman, Jaromił; Kevrekidis, Ioannis G.: Optimal deterministic algorithm generation (2018)
  15. Quirynen, Rien; Gros, Sébastien; Diehl, Moritz: Inexact Newton-type optimization with iterated sensitivities (2018)
  16. Singh, Gurpreet; Pencheva, Gergina; Wheeler, Mary F.: An approximate Jacobian nonlinear solver for multiphase flow and transport (2018)
  17. Chen, ChuanMiao; Hu, HongLing: Global existence of real roots and random Newton flow algorithm for nonlinear system of equations (2017)
  18. Grande, Jörg: Analysis of highly accurate finite element based algorithms for computing distances to level sets (2017)
  19. Hackbusch, Wolfgang; Kressner, Daniel; Uschmajew, André: Perturbation of higher-order singular values (2017)
  20. 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)

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