Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Jay Weedon Posts: 23 Registered: 12/7/04
Making a matrix positive-definite
Posted: Sep 14, 2000 2:18 PM

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?

TIA,
Jay Weedon.

Date Subject Author
9/14/00 Jay Weedon
9/14/00 Leonardo Kammer