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From luc.maison...@free.fr
Subject Re: [math] 2.1 Release plan
Date Mon, 15 Mar 2010 08:39:01 GMT

----- "Dimitri Pourbaix" <pourbaix@astro.ulb.ac.be> a écrit :

> Luc,
> 
> > I think there are two parts in the isse.
> > The first one is related to sparse matrix and we don't have an
> answer
> > yet. The second part is related to compute a partial set of
> singular
> > values. This is used for example in image compression or to find a
> > matrix with reduce rank that is the closest possible to an input
> matrix.
> > for this part, we may have an answer.
> 
> What do you mean by partial set of singular values?  If you mean
> setting
> all the singular values which are either below some threshold, of
> index
> above some value (rank), ... to zero and to compute the resulting
> product
> as an approximation of the original matrix, this is no longer the
> business
> of SVD but rather the user business as (s)he decides what (s)he does
> with
> the decomposition.  However, one could add a method to SVD which
> would
> return such a 'product'.

This is the business of SVD. See for example <http://public.lanl.gov/mewall/kluwer2002.html>,
or <http://www2.imm.dtu.dk/~pch/Projekter/tsvd.html>, or even <http://en.wikipedia.org/wiki/Singular_value_decomposition#Matrix_approximation>
and <http://en.wikipedia.org/wiki/Singular_value_decomposition#Reduced_SVDs>.

The point in these methods is not to have an exact representation of A = USVt but to truncate
it in order to have a matrix A' with some interesting properties. If the initial matrix has
a very large dimension, rather than computing the full decomposition and later withdrawing
smaller singular values and associated vectors, we prefer to not compute them.

Luc

> 
> Regards,
>   Dim.
> ----------------------------------------------------------------------------
> Dimitri Pourbaix                         *
> Institut d'Astronomie et d'Astrophysique *      Don't worry, be happy
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> mailto:pourbaix@astro.ulb.ac.be
> 
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