[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.
-------------- next part --------------
A non-text attachment was scrubbed...
Name: signature.asc
Type: application/pgp-signature
Size: 818 bytes
Desc: not available
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20151201/704cc5ce/attachment.pgp>

More information about the petsc-users mailing list