GAP theory question

[iagraso]

I am studying the theory behind GAP and I have come across different formulations for doing Gaussian process regression, specially one where the coefficients of the function are computed explicitly and one where the coefficients are not computed explicitly. In the latter, a prediction is made only on one new point by inverting the covariance matrix, without computing the coefficients of the fit.

I was wondering whether GAP computes the coefficients directly when training the potential or whether it saves the inversion of the covariance matrix in the training to then do a prediction in a new point. Could be neither of this, if so, what does GAP save once the potential is trained?. I am aware of the sparsification procedure but I am trying to understand well the basics.