The Conjugate Gradient Method Vs. The Locally Optimal Steepest Descent Method
In both the original and the preconditioned conjugate gradient methods one only needs to always set in order to turn them into locally optimal, using the line search, steepest descent methods. With this substitution, vectors are always the same as vectors, so there is no need to store vectors . Thus, every iteration of these steepest descent methods is a bit cheaper compared to that for the conjugate gradient methods. However, the latter converge faster, unless a (highly) variable preconditioner is used, see above.
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