[SciPy-User] preconditioned conjugate gradient

[Charles R Harris]

On Tue, Feb 23, 2010 at 12:14 PM, Jake VanderPlas <jakevdp at gmail.com> wrote:

> 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!
>

How did you compute the condition number and why is it so large?

Chuck
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