Re: [ublas] Solver recommendation

From: Karl Meerbergen (Karl.Meerbergen_at_[hidden])
Date: 2008-03-06 10:24:49

Jens Seidel wrote:

>On Thu, Mar 06, 2008 at 03:54:10PM +0100, Jonas wrote:
>  
>
>>On Thu, Mar 6, 2008 at 3:11 PM, Jens Seidel <jensseidel_at_[hidden]> wrote:
>>    
>>
>>>On Thu, Mar 06, 2008 at 02:32:50PM +0100, Jonas wrote:
>>> > Which library/solver (that has uBLAS bindings, preferrably) would you
>>> > recommend for solving a very sparse, real system Ax = b with size on
>>> > the order of 10^5? My initial guess from monitoring the list would be
>>> > umfpack. Would that be a good candidate?
>>>      
>>>
>>I forgot to mention that the system is overdetermined, if that is of
>>any help. BTW, sorry for top-posting.
>>    
>>
>
>This means it is non square (n x m, more rows than columns), right?
>If it has much fewer columns (m) one could easily multiply the system with
>the transposed matrix to get a square m x m matrix. Would this matrix have
>maximal rank, only positive eigenvalues? If yes, I would suggest
>starting with a simple conjugate gradient (CG) method.
>
>How much do n and m differ? If both are of the order 10^5 than it is
>already too large for Cholesky or Gaussian elimination.
>  
>

This is, of course, only true for dense or highly dense matrices.
Both Umfpack and MUMPS (for which bindings exist) such factorizations 
are feasible.

There are also sparse QR factorizations which are excellent for 
overdetermined systems, but I have no experience with them and no idea 
about free software.

Karl

>Mmh, to be honest I mainly know solvers for symmetric, positive definite
>matrices, resulting from PDE discretisations. The orign of a matrix is
>also nearly always important to properly solve it.
>
>Jens
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