Efficient randomized tensor-based algorithms for function approximation and low-rank kernel interactions
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DOI10.1007/S10444-022-09979-7zbMATH Open1505.65184arXiv2107.13107OpenAlexW3183480749MaRDI QIDQ2093707
Author name not available (Why is that?)
Publication date: 27 October 2022
Published in: (Search for Journal in Brave)
Abstract: In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to accomplish the tensor compression, provide a detailed analysis of the computational costs, provide insight into the error of the resulting approximations, and discuss the benefits of the proposed approaches. We also apply the tensor-based function approximation to develop low-rank matrix approximations to kernel matrices that describe pairwise interactions between two sets of points; the resulting low-rank approximations are efficient to compute and store (the complexity is linear in the number of points). We have detailed numerical experiments on example problems involving multivariate function approximation, low-rank matrix approximations of kernel matrices involving well-separated clusters of sources and target points, and a global low-rank approximation of kernel matrices with an application to Gaussian processes.
Full work available at URL: https://arxiv.org/abs/2107.13107
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