Conjugate gradient (CG) is an iterative minimization algorithm. We employ two versions of CG to accelerate our implementation of LR, and to overcome various numerical problems. These versions will be distinguished by the names linear CG and nonlinear CG. Before describing these methods and explaining the remarkable efficiency of linear CG, we motivate our discussion using quadratic forms and a simpler iterative minimizer known as the method of Steepest Descent.