Re: least square solution of b = A * x with a very huge A matrix

[andrea console]

Thank you Pascal.

As I see, I have a lot of iterative techniques for resolving a linear problem. How can I choose the better one for my particular system? And what about preconditioning matrix?

2013/6/1 CdeMills <address@hidden>

andrea console wrote

> Hi to all,
> I'm not a mathematician, but I have to solve this A*x=b problem. Since I'm
> working with high resolution "fit" files (images), the related matrices
> are
> very huge but sparse. I tried x = A\b, but it  gives the error: "SparseQR:
> sparse matrix QR factorization filled" that I don't understand.

If the direct method (i.e. using kind-of inversion) doesn't work, you have
alternatives with iterative methods. There are a number of variations around
the conjugate gradient method: bi-conjugate, ... Have a look at cgs, bicg,
bicgstab info pages. The difficult point is to find a good preconditionner;
Octave still lacks ilu (non-symmetric A) and ichol (symetric A), but work is
ongoing. If your matrix is diagonal dominant, a simple choice is
diag(sqrt(diag(A)))

Regards

Pascal



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