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 263 articles , 2 standard articles )

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  1. Argyros, Ioannis K.; Magreñán, Á. Alberto; Moreno, Daniel; Orcos, Lara; Sicilia, Juan Antonio: Weaker conditions for inexact mutitpoint Newton-like methods (2020)
  2. Hamon, François P.; Mallison, Bradley T.: Fully implicit multidimensional hybrid upwind scheme for coupled flow and transport (2020)
  3. Hao, Wenrui; Zheng, Chunyue: An adaptive homotopy method for computing bifurcations of nonlinear parametric systems (2020)
  4. Kopaničáková, Alena; Krause, Rolf: A recursive multilevel trust region method with application to fully monolithic phase-field models of brittle fracture (2020)
  5. Li, Qiuqi; Zhang, Pingwen: A variable-separation method for nonlinear partial differential equations with random inputs (2020)
  6. Nisha, Shwet; Parida, P. K.: Super-Halley method under majorant conditions in Banach spaces (2020)
  7. Shamanskiy, Alexander; Gfrerer, Michael Helmut; Hinz, Jochen; Simeon, Bernd: Isogeometric parametrization inspired by large elastic deformation (2020)
  8. Sheth, Soham; Moncorgé, Arthur; Younis, Rami: Localized linear systems for fully implicit simulation of multiphase multicomponent flow in porous media (2020)
  9. Argyros, Ioannis K.; George, Santhosh: Kantorovich-like convergence theorems for Newton’s method using restricted convergence domains (2019)
  10. De Leo, Roberto: Conjectures about simple dynamics for some real Newton maps on (\mathbbR^2) (2019)
  11. García, G.: Approximating roots of nonlinear systems by (\alpha)-dense curves (2019)
  12. Georg, Niklas; Ackermann, Wolfgang; Corno, Jacopo; Schöps, Sebastian: Uncertainty quantification for Maxwell’s eigenproblem based on isogeometric analysis and mode tracking (2019)
  13. Gong, Shihua; Cai, Xiao-Chuan: A nonlinear elimination preconditioned inexact Newton method for heterogeneous hyperelasticity (2019)
  14. Götschel, Sebastian; Minion, Michael L.: An efficient parallel-in-time method for optimization with parabolic PDEs (2019)
  15. Hoppe, Ronald H. W.; Linsenmann, Christopher: (\mathrmC^0)-interior penalty discontinuous Galerkin approximation of a sixth-order Cahn-Hilliard equation modeling microemulsification processes (2019)
  16. Jarlebring, Elias: Broyden’s method for nonlinear eigenproblems (2019)
  17. Potschka, Andreas: Backward step control for Hilbert space problems (2019)
  18. Sun, Tianxiao; Quoc, Tran-Dinh: Generalized self-concordant functions: a recipe for Newton-type methods (2019)
  19. van der Vegt, J. J. W.; Xia, Yinhua; Xu, Yan: Positivity preserving limiters for time-implicit higher order accurate discontinuous Galerkin discretizations (2019)
  20. Zhang, Xiaolong; Boyd, John P.: Revisiting the Thomas-Fermi equation: accelerating rational Chebyshev series through coordinate transformations (2019)

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