TY - JOUR T1 - A Kernel-Independent Sum-of-Gaussians Method by de la Vallée-Poussin Sums AU - Liang , Jiuyang AU - Gao , Zixuan AU - Xu , Zhenli 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 Vallée-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 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.