LDU decomposition - sparse matrix

[Hassan2]

I have a large sparse symmetric matrix and I'd like to know the number of its negative eigenvalues. To this end, I should perform an LDL^T decomposition of the matrix and count the number of negative diagonal entries of the D matrix. This would be equal to the number of negative eigenvalues.

Since I need the diagonal matrix D only, is there an efficient way to acquire D without saving L ? My matrix is large and only the nonzero entries are stored. I can't store the dense lower matrix L.

Your help is appreciated.

 

[fresh_42]

Maybe algorithms for the similar Cholesky decomposition can help. They are at least stable.