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


From: CdeMills
Subject: Re: least square solution of b = A * x with a very huge A matrix
Date: Sat, 1 Jun 2013 04:57:52 -0700 (PDT)

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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