On Sep 21, 2014, at 12:35 PM, De Groof, Vincent Frans Maria <[email protected]> wrote:
> Hi all, > > > the natural norm for positive definite systems in Petsc uses the > preconditioner B, and is defined by r' * B * r. Am I right assuming that this > way we want to obtain an estimate for r' * K^-1 * r, which is impossible > since we don't have K^-1? But we do know B which is approximately K^-1. I think so. The way I look at it is r’ * B * r = e’ *A *B *A e and if B is inv(A) then it = e’*A*e which is the “energy” of the error as measured by A, .ie. ||e||_A = sort(e’*A*e) . Now, for example, if B = I then one gets e’*A*A*e so it is no longer the “natural norm” of the error, just some other norm. > > > I'm sorry for this, I guess, basic question, but I just wanted to be sure. > > > kind regards, > Vincent
