Re: QR vs LU factorisation

[Vic Norton]

Hi Jordi,

I doubt that QR is any better than LU if the matrix is very poorly  
conditioned. SVD is the best solution in this case. For example, to  
invert a matrix A choose an svd "precision", say

   svdcut = 1e-12;

Then do

   [U S V] = svd(A, 1);
   sig = diag(S);
   rnk = 0;
   for i = 1 : length(sig)
      if sig(i)/sig(1) < svdcut; break; endif
      rnk++;
   endfor
   Ainv = ( V(:, 1:rnk) * diag(1 ./ sig(1:rnk)) ) * U(:, 1:rnk)';

to get the (pseudo)inverse of A.

Regards,

Vic


On Jun 29, 2008, at 2:24 PM, Jordi Gutiérrez Hermoso wrote:

> This isn't specifically an Octave question except tangentially.
>
> I have some matrices that are as bad as can be: largish (1000x1000 or
> so), full, unsymmetric, and ill-conditioned. I notice that Octave uses
> LU factorisation with partial pivoting to invert these matrices as a
> last resort, which has been giving me acceptable results. Someone
> suggested to me that QR factorisation would be better suited. I'm
> reading Golub & Van Loan, but see no clear indication of when to use
> QR or LU.
>
> Does anyone have any suggestions?
>
> Thanks,
> - Jordi G. H.
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