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

2015/05/21 by Dishi Liu, Liu, Dishi, Hermann G. Matthies +1 · 1 citation
Computer Science · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Scientific Research and Discoveries

paper · pdf · doi:10.48550/arxiv.1505.06195

openalex publication_date 2015/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Large kernel systems are prone to be ill-conditioned. Pivoted Cholesky decomposition (PCD) render a stable and efficient solution to the systems without a perturbation of regularization. This paper proposes a new PCD algorithm by tuning Cross Approximation (CA) algorithm to kernel matrices which merges the merits of PCD and CA, and proves as well as numerically exemplifies that it solves large kernel systems two-order more efficiently than those resorts to regularization. As a by-product, a diagonal-pivoted CA technique is also shown efficient in eigen-decomposition of large covariance matrices in an uncertainty quantification problem.

Cited by

• Novel Pivoted Cholesky Decompositions for Efficient Gaussian Process Inference

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