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Topic: Making a matrix positive-definite
Replies: 9   Last Post: Sep 16, 2000 2:51 PM

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Jay Weedon

Posts: 23
Registered: 12/7/04
Making a matrix positive-definite
Posted: Sep 14, 2000 2:18 PM
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Hi folks,

I'm implementing a statistical algorithm that solves a maximization
problem iteratively.

After convergence, the procedure generates a "negative hessian" matrix
I'll call -H.

If the algorithm converged at a local max., the eigenvalues of -H are
supposed to be all positive. The inverse of -H can then be used as a
parameter covariance matrix.

My problem is this: The algorithm converges, and -H (which is of
approx. dimension 35x35) has ALMOST all positive eigenvalues. The
largest is about +1e4, ranging down to +1e-5, but there's ONE that's
-1e-9. Inverting -H yields a couple of negative parameter variances,
which are uninterpretable.

My guess is that I do in fact have a max, but that rounding error etc.
is responsible for this tiny negative eigenvalue. I've tried to fiddle
with some precision parameters but can't get rid of it.

I THINK that what I'd like to do now is to find a perturbation of -H
that's very small, but large enough to make it positive-definite so
that all my variances will be positive. Anyone know how to do this?
Does my suggestion make any sense?

Jay Weedon.

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