Sensitivity conjugate gradients method

The basic difficulty with the steepest descent method is that it is too sensitive to the scaling of/(x), so that convergence is very slow and what amounts to oscillation in the x space can easily occur. For these reasons steepest descent or ascent is not a very effective optimization technique. Fortunately, conjugate gradient methods are much faster and more accurate. 

The descent condition is used to define the algorithmic sequence that generates p but is not always tested in practice. In reality, numerical errors can lead to departure from theoretical expectations. Thus, it is often necessary to check explicitly for the descent property of p t from equation (10), especially in nonlinear conjugate gradient methods which are very sensitive to roundoff. 

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