[Trilinos-Users] Correction (Two questions on the smoother of a multilevel preconditioner)

Ernesto Prudencio prudenci at slac.stanford.edu
Tue Jan 15 15:12:04 MST 2008


Sorry for the confusion:

Ax* = b; e(k) = x* - x(k); r(k) = b - A x(k) = A e(k); B = precondtioner.

Damped preconditioned Richardson: x(k+1) = x(k) + \eta B r(k)

Rewriting: e(k+1) = e(k) - \eta B r(k) = [I - \eta B A] e(k) = E e(k)

The questions, though, remain the same.

Thanks in advance,

Ernesto.

On Tue, 15 Jan 2008, Ernesto Prudencio wrote:

>
> Hi.
>
> On page 25 of "ML 5.0 Smoothed Aggregation User's Guide" there is the 
> explanation for the option "smoother: Aztec as solver". If this options is 
> set to 'false', then "only the Aztec's preconditioner function will be used 
> as smoother".
>
> Question 1: Is it correct to interpret the 'false' option as a preconditioned 
> Richardson smoother which iterates as many times as determined by "smoother: 
> sweeps" option?
>
> By a (damped) preconditioned Richardson iteration I mean [notation: Ax = b; 
> r(k) = b - A x(k); B = preconditioner operator; \eta = dumping factor]:
>
> r(k+1) = (I - \eta A B) r(k) = E r(k),
>
> where E = error propagation matrix.
>
> Question 2: Does the "smoother: damping factor" parameter correspond to the 
> "\eta" parameter above?
>
> Thanks,
>
> Ernesto.
>
>
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