[petsc-users] newbie questions on preconditioner LU

[Jed Brown]

On Mon, Jan 28, 2013 at 1:01 PM, Matthew Knepley <knepley at gmail.com> wrote:

> M^(-1) * A x = M^(-1) * b
>>
>> where, M is the preconditioning matrix and in many cases, we just use A
>> as the preconditioning matrix.
>>
>>
>> Question:
>> 1), Is the understanding above correct?
>>
>
> This is too simplistic. If you really mean M^{-1}, then no, you (almost)
> never use A as M. If you mean an
> approximate inverse to M, then yes.
>

Specifically, the notation "M^{-1}" indicates a matrix M exists and that we
are applying its inverse. In practice, M is never computed explicitly. In
the case of incomplete factorization, M "exists" in that it is equal to
L*U, but we still don't form it explicitly, we just apply it as M^{-1} x =
U^{-1} (L^{-1} x).
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