Conjugate gradient method

Conjugate gradient method is used in two ways.

1) Solving an optimization problem: obtaining the condition to minimize some function.
2) Solving a system of linear equations.

2) is an application of 1). First define a function which gets minimum when the equations is satisfied, then using 1), get the condition = the answer of the equations..

An excellent document about conjugate gradient method.
"An Introduction to the Conjugate Gradient Method Without the Agonizing Pain"
www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf
Anybody who starts learning conjuagate gradient method should start here.
This document should be registered as a world heritage.