My personal experience is to use approximate eigenvectors to deflate conjugate gradient. In that regard, it is kinda like DGMRES, except that the iterative method is different. A lot of situations I have seen use eigenvectors, but just as what Vuik does, you never know when someone will propose something unconventional. Deflation being a general framework, it does not hurt (from a user's point of view) to add something to the library and let the user play. Jie ----- Original Message ----- From: "Matthew Knepley" <[email protected]> To: "For users of the development version of PETSc" <[email protected]> Sent: Wednesday, February 27, 2013 4:05:47 AM Subject: Re: [petsc-dev] Deflated Krylov solvers for PETSc I think the problem with that approach to deflation is preconditioning, unless you use injection as Vuik does. You can easily get this kind of projection by using MatShell. I tried Ronald Morgan's stuff when I was in grad school and it never made a bit of difference. Is there any situation where deflation is useful and cannot be phrased as our current MG? Matt