The conjugate gradient method is an algorithm for finding the nearest local minimum of a function of  variables which presupposes that the gradient of the function can be computed. It uses conjugate directions instead of the local gradient for going downhill. If the vicinity of the minimum has the shape of a long, narrow valley, the minimum is reached in far fewer steps than would be the case using the method of steepest descent.

For a discussion of the conjugate gradient method on vector and shared memory computers, see Dongarra et al. (1991). For discussions of the method for more general parallel architectures, see Demmel et al. (1993) and Ortega (1988) and the references therein.

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