A Kernel-Independent Sum-of-Gaussians Method by de la Vallée-Poussin Sums

A Kernel-Independent Sum-of-Gaussians Method by de la Vallée-Poussin Sums

Year:    2021

Author:    Jiuyang Liang, Zixuan Gao, Zhenli Xu

Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 5 : pp. 1126–1141

Abstract

Approximation of interacting kernels by sum of Gaussians (SOG) is frequently required in many applications of scientific and engineering computing in order to construct efficient algorithms for kernel summation or convolution problems. In this paper, we propose a kernel-independent SOG method by introducing the de la Vallée-Poussin sum and Chebyshev polynomials. The SOG works for general interacting kernels and the lower bound of Gaussian bandwidths is tunable and thus the Gaussians can be easily summed by fast Gaussian algorithms. The number of Gaussians can be further reduced via the model reduction based on the balanced truncation based on the square root method. Numerical results on the accuracy and model reduction efficiency show attractive performance of the proposed method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2020-0254

Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 5 : pp. 1126–1141

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    Sum-of-Gaussians approximation interaction kernels de la Vallée-Poussin sums model reduction.

Author Details

Jiuyang Liang

Zixuan Gao

Zhenli Xu