Volume 13, Issue 5
A Kernel-Independent Sum-of-Gaussians Method by de la Vallee-Poussin Sums

Jiuyang Liang, Zixuan Gao & Zhenli Xu

Adv. Appl. Math. Mech., 13 (2021), pp. 1126-1141.

Published online: 2021-06

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  • 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 Vallee-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.


  • Keywords

Sum-of-Gaussians approximation, interaction kernels, de la Vallee-Poussin sums, model reduction.

  • AMS Subject Headings

65D15, 42A16, 70F10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-13-1126, author = {Jiuyang Liang , and Zixuan Gao , and Zhenli Xu , }, title = {A Kernel-Independent Sum-of-Gaussians Method by de la Vallee-Poussin Sums}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {13}, number = {5}, pages = {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 Vallee-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.


}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0254}, url = {http://global-sci.org/intro/article_detail/aamm/19256.html} }
TY - JOUR T1 - A Kernel-Independent Sum-of-Gaussians Method by de la Vallee-Poussin Sums AU - Jiuyang Liang , AU - Zixuan Gao , AU - Zhenli Xu , JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1126 EP - 1141 PY - 2021 DA - 2021/06 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2020-0254 UR - https://global-sci.org/intro/article_detail/aamm/19256.html KW - Sum-of-Gaussians approximation, interaction kernels, de la Vallee-Poussin sums, model reduction. AB -

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 Vallee-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.


Jiuyang Liang, Zixuan Gao & Zhenli Xu. (1970). A Kernel-Independent Sum-of-Gaussians Method by de la Vallee-Poussin Sums. Advances in Applied Mathematics and Mechanics. 13 (5). 1126-1141. doi:10.4208/aamm.OA-2020-0254
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