Conjugate gradient methods
Author: Erik Zuehlke
Stewards: Dajun Yue and Fengqi You
The conjugate gradient method is a mathematical technique that can be useful for the optimization of a non-linear system. This technique is generally used as an iterative algorithm, however, it can be used as a direct method, and it will produce a numerical solution. Generally this method is used for very large systems where it is not practical to solve with a direct method. This method was developed by Magnus Hestenes and Eduard Stiefel.
The iterative version of the conjugate gradient method
Will put equation in for final. Also an image on the right of the page showing a basic version of the method. Direct method may also be included if it is found to be necessary.
Numerical Example of the method
Will create a problem and demonstrate it using equations here as well.
 Straeter, T. A. "On the Extension of the Davidon-Broyden Class of Rank One, Quasi-Newton Minimization Methods to an Infinite Dimensional Hilbert Space with Applications to Optimal Control Problems". NASA Technical Reports Server. NASA. Retrieved 10 October 2011.