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Large kernel systems are prone to be ill-conditioned. Pivoted Choleskydecomposition (PCD) render a stable and efficient solution to the systemswithout a perturbation of regularization. This paper proposes a new PCDalgorithm by tuning Cross Approximation (CA) algorithm to kernel matrices whichmerges the merits of PCD and CA, and proves as well as numerically exemplifiesthat it solves large kernel systems two-order more efficiently than thoseresorts to regularization. As a by-product, a diagonal-pivoted CA technique isalso shown efficient in eigen-decomposition of large covariance matrices in anuncertainty quantification problem.

Pivoted Cholesky decomposition by Cross Approximation for efficient solution of kernel systems