----- "Dimitri Pourbaix" <pourb...@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 > CP 226, office 2.N4.211, building NO * and CARPE DIEM. > Universite Libre de Bruxelles * > Boulevard du Triomphe * Tel : +32-2-650.35.71 > B-1050 Bruxelles * Fax : > +32-2-650.42.26 > http://sb9.astro.ulb.ac.be/~pourbaix * > mailto:pourb...@astro.ulb.ac.be > > --------------------------------------------------------------------- > To unsubscribe, e-mail: dev-unsubscr...@commons.apache.org > For additional commands, e-mail: dev-h...@commons.apache.org --------------------------------------------------------------------- To unsubscribe, e-mail: dev-unsubscr...@commons.apache.org For additional commands, e-mail: dev-h...@commons.apache.org
