An asymptotic evaluation is then possible along the lines of the linear stationary phase / steepest descent method.
2.
Thus, every iteration of these steepest descent methods is a bit cheaper compared to that for the conjugate gradient methods.
3.
In both the original and the preconditioned conjugate gradient methods one only needs to set \ beta _ k : = 0 in order to make them locally optimal, using the line search, steepest descent methods.
4.
A ( properly speaking ) nonlinear steepest descent method was introduced by Kamvissis, K . McLaughlin and P . Miller in 2003, based on previous work of Lax, Levermore, Deift, Venakides and Zhou.
5.
The mathematical explanation of the better convergence behavior of the method with the Polak Ribi�re formula is that the method is "'locally optimal "'in this case, in particular, it does not converge slower than the locally optimal steepest descent method.
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