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(adsbygoogle = window.adsbygoogle || []).push({}); ^{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.

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# LDU decomposition - sparse matrix

Can you offer guidance or do you also need help?

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