On Thu, Feb 25, 2010 at 5:38 PM, <scipy-user-request@scipy.org> wrote:

---------- Forwarded message ---------- From: Jake VanderPlas <jakevdp@gmail.com> To: scipy-user@scipy.org Date: Tue, 23 Feb 2010 11:14:53 -0800 Subject: [SciPy-User] preconditioned conjugate gradient Hello, I'm looking for a method to solve a sparse linear equation A*x=b, where A is a NxN symmetric scipy.sparse.LinearOperator object, and b is a 1D numpy vector. The obvious choice would be something like scipy.sparse.linalg.cg. The problem is, the condition number of A is very large - on order of 10^26. From a search through relevant literature, I know that matlab's preconditioned conjugate gradient (pcg) routine works well for the type of problem I'm dealing with. Is there any similar routine in scipy? I've looked at scipy.sparse.linalg.eigen.lobpcg, which seems to be along the lines of what I need. I could use this to find the inverse, but that would involve computing an NxN dense matrix of eigenvectors, which will cause memory problems in my case. Any help would be appreciated! -Jake

Note that your matrix A must also be (positive or negative) definite, or the conjugate gradient method may break down. If A is indefinite, you will probably be safer with MINRES, CRAIG or SYMMLQ. As another reader pointed out, you still need to supply a good preconditioner. Often, the application suggests the kind of preconditioner that works well. -- Dominique