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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?
Heber
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**tolerance for eigenvalue decomposition**,
*Heber Farnsworth* **<=**