QuasiNewton
There are many different Quasi-Newton Methods. Code for all of these methods covered in this repository is written in Julia and can be found at QuasiNewton.jl. This program can be run online via repl.it. To run locally, have Julia installed and run the command julia QuasiNewton.jl in the directory where the program is saved.
The video covering this method can be found here.
Reference links:
- Wolfe's paper https://doi.org/10.1145/368518.368542
- Bittner's paper - Technische Universität Dresden
- Tornheim's paper https://doi.org/10.1145/321217.321224
- Barnes's paper https://doi.org/10.1093/comjnl/8.1.66
- Brent's papers https://doi.org/10.1137/0710031 and https://doi.org/10.1007/978-1-4684-2001-2_7
The video covering these methods can be found here.
Reference links:
- Brent's paper https://doi.org/10.1137/0710031
- Ortega and Rheinboldt books.google.com
- Korganoff's book "Méthodes de calcul numérique: Algèbre non linéaire, Vol 1" [wordlcat](https://www.worldcat.org/title/methodes-de-calcul-numerique/oclc/848108709]
- Robinson's paper https://epubs.siam.org/doi/abs/10.1137/0703057
The video covering this method can be found here.
Reference links:
- "Iterative Methods for the Solution of Equations" by J. F. Traub archive.org
- Soleymani et. al. https://doi.org/10.1155/2014/705375
The video covering this method can be found here.
The video covering this method can be found here.
Reference links:
- "A class of methods for solving nonlinear simultaneous equations" by Charles G. Broyden https://doi.org/10.2307/2003941
- "A faster Broyden method" by Kvaalen https://doi.org/10.1007/BF01931297
- "On Some Methods Based on Broyden's Secant Approximation to the Hessian" by Dennis https://hdl.handle.net/1813/5946
- "On the discovery of the 'good Broyden' method" by C. G. Broyden https://doi.org/10.1007/s101070050111
- "The convergence of an algorithm for solving sparse nonlinear systems" by C. G. Broyden https://www.ams.org/
- "On the Local and Superlinear Convergence of Quasi-Newton Methods" by Broyden, Dennis, and Moré https://doi.org/10.1093/imamat/12.3.223
- "Some Convergence Properties of Broyden's Method" by Gay https://doi.org/10.1137/0716047
- "Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix" by Sherman and Morrison https://www.jstor.org/stable/2236561