Conjugate gradient methods

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Author: Erik Zuehlke
Stewards: Dajun Yue and Fengqi You

Magnus Hestenes one of the creators of the Conjugate Gradient Method [1]

Contents

Introduction

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.[1]

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.


References

[1] 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.