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 298 articles , 2 standard articles )

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  1. Argyros, Ioannis K.: Weaker convergence criteria for Traub’s method (2022)
  2. Duff, Timothy; Hein, Nickolas; Sottile, Frank: Certification for polynomial systems via square subsystems (2022)
  3. Luo, Xin-long; Xiao, Hang; Lv, Jia-hui: Continuation Newton methods with the residual trust-region time-stepping scheme for nonlinear equations (2022)
  4. Augustin, Christoph M.; Gsell, Matthias A. F.; Karabelas, Elias; Willemen, Erik; Prinzen, Frits W.; Lumens, Joost; Vigmond, Edward J.; Plank, Gernot: A computationally efficient physiologically comprehensive 3D-0D closed-loop model of the heart and circulation (2021)
  5. Cătinaş, Emil: How many steps still left to (x)? (2021)
  6. Hanke, Michael; März, Roswitha: Convergence analysis of least-squares collocation methods for nonlinear higher-index differential-algebraic equations (2021)
  7. Hoppe, Ronald H. W.; Pahari, Basanta R.; Winkle, James J.: Numerical simulation of the formation of spherulites in polycrystalline binary mixtures (2021)
  8. Jamal, Farrukh; Chesneau, Christophe; Aidi, Khaoula; Ali, Aqib: Theory and application of the power Ailamujia distribution (2021)
  9. Kodnyanko, Vladimir: Improved bracketing parabolic method for numerical solution of nonlinear equations (2021)
  10. Kulchytska-Ruchka, Iryna; Schöps, Sebastian: Efficient parallel-in-time solution of time-periodic problems using a multiharmonic coarse grid correction (2021)
  11. Lemoine, Jérôme; Marín-Gayte, Irene; Münch, Arnaud: Approximation of null controls for semilinear heat equations using a least-squares approach (2021)
  12. Lemoine, Jérôme; Münch, Arnaud: A fully space-time least-squares method for the unsteady Navier-Stokes system (2021)
  13. Lemoine, Jérôme; Münch, Arnaud: Resolution of the implicit Euler scheme for the Navier-Stokes equation through a least-squares method (2021)
  14. Liu, Lulu; Keyes, David E.: Approximate error bounds on solutions of nonlinearly preconditioned PDEs (2021)
  15. Luo, Xin-long; Xiao, Hang: Generalized continuation Newton methods and the trust-region updating strategy for the underdetermined system (2021)
  16. Naceur, Nahed; Alaa, Nour Eddine; Khenissi, Moez; Roche, Jean R.: Theoretical and numerical analysis of a class of quasilinear elliptic equations (2021)
  17. Ontañón, Santiago; Alcubierre, Miguel: Rotating boson stars using finite differences and global Newton methods (2021)
  18. Schiela, Anton; Ortiz, Julian: An SQP method for equality constrained optimization on Hilbert manifolds (2021)
  19. Shamanskiy, Alexander; Simeon, Bernd: Mesh moving techniques in fluid-structure interaction: robustness, accumulated distortion and computational efficiency (2021)
  20. Timme, Sascha: Mixed precision path tracking for polynomial homotopy continuation (2021)

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