On the low-rank approximation by the pivoted Cholesky decomposition

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Multi-output separable Gaussian process: Towards an efficient, fully Bayesian paradigm for uncertainty quantification (2013, methodology): “For this reason, one has to use a low-rank approximation of Cd(n) using the pivoted Cholesky factorization [32].”
First order second moment analysis for stochastic interface problems based on low-rank approximation (2013, methodology): “Exponential convergence rates in m are proven under the assumption that the eigenvalues of C exhibit a sufficiently fast exponential decay, see [21].”
Tensor-Structured Factorized Calculation of Two-Electron Integrals in a General Basis (2013, unknown): “We refer to [16, 8, 13, 4, 37, 35] for more details on the algebraic aspects of matrix Cholesky decomposition and the related ACA techniques.”
GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration (2018, methodology): “In proving convergence bounds for our preconditioner we explicitly make use of some theoretical results from [19] (see Appendix D).”
On Sampling Spatially-Correlated Random Fields for Complex Geometries (2019, methodology): “…we apply the low-rank pivoted Cholesky decomposition to replace the (large) matrix A ∈ R N × N by the low-rank matrix A m := L m L T m , with L m ∈ R N × m and such that A − A m < ε [10]. the k k In general, the performance of the method strongly depends on decay rate of the spectrum of A .”