sva
===

singular value approximation



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [U,s,V]=sva(A,k)
    [U,s,V]=sva(A,tol)




Arguments
~~~~~~~~~

:A real or complex matrix
: :k integer
: :tol nonnegative real number
:



Description
~~~~~~~~~~~

Singular value approximation.

`[U,S,V]=sva(A,k)` with `k` an integer >=1, returns `U,S` and `V` such
that `B=U*S*V'` is the best L2 approximation of `A` with rank( `B`)=
`k`.

`[U,S,V]=sva(A,tol)` with `tol` a real number, returns `U,S` and `V`
such that `B=U*S*V'` such that L2-norm of `A-B` is at most `tol`.



Examples
~~~~~~~~


::

    A=`rand`_(5,4)*`rand`_(4,5);
    [U,s,V]=sva(A,2);
    B=U*s*V';
    `svd`_(A)
    `svd`_(B)
    `clean`_(`svd`_(A-B))




See Also
~~~~~~~~


+ `svd`_ singular value decomposition


.. _svd: svd.html