Regularization of a matrix that has some tiny negative eigenvalues

Dear all:

In what I am doing I sometimes get a (Hessian) matrix that has a
couple of tiny negative eigenvalues (e.g. -6 * 10^-17). So, I can't
run a Cholesky decomp on it - but I need to.
Is there an established way to regularize my (Hessian) matrix (e.g.,
via some transformation) that would allow me to get a semi-positive
definite matrix to be used in Cholesky decomp?

Or should I try some other decomp method on the back end that is less
sensitive than Cholesky?
Dimitri

The Matrix package (which should already be insatlled on your
computer, since it is "Recommended") have the function
nearPD, which should do the job.

Kjetil

On Sat, Jan 29, 2011 at 1:32 AM, Dimitri Liakhovitski
<dimitri.liakhovitski at gmail.com> wrote:

Dear all:

In what I am doing I sometimes get a (Hessian) matrix that has a
couple of tiny negative eigenvalues (e.g. -6 * 10^-17). So, I can't
run a Cholesky decomp on it - but I need to.
Is there an established way to regularize my (Hessian) matrix (e.g.,
via some transformation) that would allow me to get a semi-positive
definite matrix to be used in Cholesky decomp?

Or should I try some other decomp method on the back end that is less
sensitive than Cholesky?
Dimitri