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On 09/24/10 11:22:20, Hauke Heibel wrote:
> Just to help me understand what is going on...
>
> Does that mean for a 3x2 the decomposition does actually create
> matrices with dimensions
>
> 3x2 2x2 2x2
That's called the "economy form" of the SVD and it's very advantageous
if there many more rows than columns. Other libraries make it an option
to compute the full or the economy form.
>
> and not
>
> 3x3 3x2 2x2 ?
>>>>SNIP
> Let me clarify what you meant with "does not have a solution". In
> fact, what I did in the unit test was sort of stupid because solving
> a
> system A*x = b where A is overdetermined will of course result in an
> x
> = pinv(A)*b such that Ax != b but where ||Ax-b||^2 is minimal. So in
> case we can guarantee that our SVD produces a solution that computes
> exactly the x which minimized ||Ax-b||, we can say it is fine though
> I
> don't know how to unit test such a system besides doing tests based
> on
> problems for which we know the correct solutions.
You can plug it into the normal equations. Computing a residual by
using the normal equations is not bad unless A has a huge norm
itself.
Helmut Jarausch
Lehrstuhl fuer Numerische Mathematik
RWTH - Aachen University
D 52056 Aachen, Germany