generating a sparse matrix with a specific singular value distribution

Hello,

I want to test an iterative algorithm on sparse matrices with
different singular value distributions. I can generate a full matrix
with a given singular value distribution by using a reverse SVD
decomposition. That is I know:

A = U*D*V' for any A, where U and V are orthogonal. I can get U and V
from a QR decomposition and supply a D with the singular values that I
want to generate A.

However, is it possible to generate a sparse matrix A in this way
(apart from generating A as above and removing elements at random)?

I would appreciate any ideas on this, thanks for your help.
.

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