Speeding up Kriging by Using Pivoted Cholesky Decomposition and Low-Rank Structures

Abstract

Kriging is often impaired in terms of costs and accuracy by ill-conditioned covariance matrices of large dimension N. We propose to tackle both of these problem by using a pivoted Cholesky decomposition (PCD) and a rank-k formulation of Kriging. The PCD solves a rank-deficient but consistent system. By reformulating the maximum likelihood training accordingly, the complexity is reduced to O(k^2N) with k <<N. In numerical tests our approach displays an accuracy comparable to regularization approaches.