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Subject: Re: solve command
Date: Wed, 25 Mar 2009 12:10:04 +0000 (UTC)
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"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <gqd172$fp1$1@fred.mathworks.com>...
> Torsten Hennig <Torsten.Hennig@umsicht.fhg.de> wrote in message <29391649.1237975774607.JavaMail.jakarta@nitrogen.mathforum.org>...
> 
> > 
> > As I read in the MATLAB documentation, the backslash
> > operation does not seem to produce a least-squares
> > solution in the case of square systems if the coefficient
> > matrix is singular.
> > 
> > Instead, you can try
> > x = pinv(A*R)*b
> > 
> > Best wishes
> > Torsten.
> 
> Hi Torsen,
> 
> Yes, the backslash actually produces the least-square solution for overdetermined system (minimizing the norm of the residual, on the image space), as with pinv.
> 
> However if the matrix has non-trivial kernel (different {0}), then backslash selects a solution that is usually not  the minimum-norm solution (minimize the norm on the source space, but sill least-square solution). This is the main difference between pinv.
> 
> Hope it is clear,
> 
> Bruno


Thanks for the clearings.
I tried to built the A Matrix in another way. So the new equation is A*x=B.
But when I try to solve this problem with x=A\B or x=inv(A)*B, then the results is not quite correct. I guess it must be a rounding error or something like that.
Is it possible solve this problem in another way, e.g. an iteration method??

Shane