Re: [ublas] nonsquare system of equations - corrected

From: Gunter Winkler (guwi17_at_[hidden])
Date: 2006-11-13 09:44:39

On Monday 13 November 2006 15:12, Sorkin Dima wrote:
> On Mon, 13 Nov 2006, Gunter Winkler wrote:
> >> LSQR problem
> >
> > 1. Tim Davis: http://www.cise.ufl.edu/research/sparse/
>
> Ok. This I should explore. I only remember this site for
> UMFPACK LU, which is for square matrices (?)

He provides a sparse QR factorization (among other direct solvers).

> It seems that the only suppoted method for nonsquare solving of
> Ax=b is A'Ax = A'x.

Solving nonsquare systems is usually expressed as an optimization problem.

a) minimize ||Ax-b|| (if rank(A)>size(x) )
b) minimize ||x|| , s.t. Ax-b=0 (if rank(A)<size(x) )

So I think one has to look for iterative optimization methods. Unfortunately I 
know very little of this topic.
Alternatively you can use the QR decomoposition to solve the above problems.

mfg
Gunter