# Estimate the diagonal of a Cholesky factor…?

I'm computing several hundred Cholesky factorizations of large, sparse matrices, and I'm really only doing Cholesky factorization because I need to know the diagonal elements of the Cholesky factor L. Does anyone know a good method for estimating the diagonal of Cholesky factors (that does not involve Cholesky factorization)?

For example: Q = L * transpose(L) D = diagonal(L)

Can I get D from Q without calculating all of L?

Thanks!

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The product of the first $k$ diagonal elements of $L$ squared is equal to the determinant of the $k\times k$ top left submatrix of $Q$. – Yoav Kallus Jun 20 '13 at 21:37
That's interesting and possibly helpful. I do need the entire diagonal of L, which would leave me taking the determinant of Q... and determinants for large, sparse, spd matrices are usually calculated via Cholesky factorization, which would put me back where I started. Any thoughts on that? – Ted Jun 21 '13 at 11:24
@Ted, in a first time, you want the diagonal of $L$. As wrote Kallus, that implies the calculation of $\det(Q)$. In a second time, you write yourselves that your question has not any interest. Finally you say " I do need the entire diagonal of L". What do you want exactly ? – loup blanc Dec 7 '13 at 13:18