The two actually look very similar. The community that I learned Uzawa from is very familiar with Sherman-Morrison. Uzawa might in fact be an iterative S-M ... the wikapedia page does not explain how to recover the solution Y and does not accommodate a non-zero RHS for the constraint equations. Both of which you'd want to do to be general.
On Nov 4, 2011, at 3:28 PM, Jed Brown wrote: > On Fri, Nov 4, 2011 at 10:08, Mark F. Adams <mark.adams at columbia.edu> > wrote: > Woodbury does not seem natural (ie, efficient) when A is solved iteratively. > These methods rely on multiple solves with A being almost the same cost as > one solve, most of the cost going into the matrix setup (factorization). > This is generally not the case with iterative solvers. How does Woodbury > work with inexact solves? It looks to me like there are rank-of-B + 2 solves > here. Uzawa solvers (iterate on Schur compliment) seem better -- they work > fine with inexact solves for A and you can precondition them easily for these > special matrices with explic (D - C diag(A)^-1 B)^-1. They converge very > fast, like one digit per iteration even w/o preconditioning in my experience. > > I think both directions are likely useful. I vaguely recall seeing Woodbury > used as a preconditioner where the low rank part was computed using an > approximate A. We already have support via PCFieldSplit for the Uzawa-type > iteration you describe and for the related full-space iteration. -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-dev/attachments/20111104/da427218/attachment.html>
