Cholesky decomposition error while eigenvalues are positive

For a Bayesian optimization I use the lower Cholesky decomposition. However, for a large interval the covariance matrices can have some zero eigenvalues which is not accepted for this decomposition. Adding a small diagonal is supposed to fix this. The eigenvalues are indeed positive but still I get an error saying the matrix is not positive definite.

Ensuring the matrix is symmetric does not help either ()

[Matt J]

What's max(eig(COV)) ?

[Niels Uitterdijk]

Large positive, 77.9.

As a sidenote, I do occasionaly get complex eigenvalues for certain intervals. Trying to fix this by forcing the matrix to be symmetric pushes the eigenvalues to be negative (-7.3).

[Niels Uitterdijk]

I ended up using an SVD, which can achieve the same result.