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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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  • $\begingroup$ 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 $Q$. $\endgroup$
    – Yoav Kallus
    Commented Jun 20, 2013 at 21:37
  • $\begingroup$ 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? $\endgroup$
    – Ted
    Commented Jun 21, 2013 at 11:24
  • $\begingroup$ @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 ? $\endgroup$
    – loup blanc
    Commented Dec 7, 2013 at 13:18

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