# Derivative of $H$ with respect to $W$

I am trying to solve a generalized linear squares model with the following form:

$\hat{Y}= X(X'\Omega^{-1}WX)^{-1}X'\Omega^{-1}WY$

$H= X(X'\Omega^{-1}WX)^{-1}X'\Omega^{-1}W$

$\Omega$ is the co-variance matrix.

$W$ is a diagonal matrix that weights a given observation $w_i$ and is normally $I$.

Occasionally a single or multiple diagonal entries in $W$ are updated.

How should a change in $W$ update $H$ without having to recompute $H$ entirely?

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The title and body don't match. –  joriki Nov 27 '12 at 11:26
Thanks for pointing that out. –  Atlas Nov 27 '12 at 11:55