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tolerance for eigenvalue decomposition

From: Heber Farnsworth
Subject: tolerance for eigenvalue decomposition
Date: Mon, 19 May 2003 23:29:11 -0500

For obscure reasons I need to do the following

[V Lambda] = eig(Q);

X = V*D*inv(V);

where V has the eigenvectors of Q and Lambda and D are diagonal
matrices.  It turns out that D is a smooth function of Lambda.  The
problem is that I am trying to choose the elements of Q to maximize a
function of X and I find that this function is not smooth.  It looks
smooth until you look very closely (as I have to when checking whether
the function is concave at the optimum.  I think what is going on is
that numerical inaccuracies begin to be a problem when you are looking
at small changes.

Is there a way to increase the accuracy of eig, or inv, or both?


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