[petsc-users] Weighted Jacobi
Jed Brown
jed at jedbrown.org
Tue Dec 1 13:46:34 CST 2015
Timothée Nicolas <timothee.nicolas at gmail.com> writes:
> I meant
>
> X^{k+1} = omega*D^{-1}*(b - (A-D)*X^k) + (1-omega)*X^k
Let's rearrange:
X^{k+1} = omega*D^{-1}*(b - A*X^k) + omega*D^{-1}*D*X^k + (1-omega)*X^k
= omega*D^{-1}*(b - A*X^k) + omega*X^k - omega*X^k + X^k
= X^k + omega*D^{-1}*(b - A*X^k)
There, isn't that simpler? This is Richardson preconditioned by Jacobi,
as Dave says.
Matt's question is about how to define D, which is available through
options to Jacobi. The diagonal is the default.
But you'll likely be happier using Chebyshev, which is strictly more
general than damped Jacobi.
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