A kernel-independent sum-of-Gaussians method by de la Vallée-Poussin sums

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 and convolution problems. In this paper, we propose a kernel-independent SOG method by introducing the de la Vall\'ee-Poussin sum and Chebyshev polynomials. The SOG works for general interacting kernels and the lower bound of bandwidths of resulted Gaussians is allowed to be tunable so that the Gaussians can be easily summed by fast Gaussian algorithms. The number of terms can be further reduced via the model reduction based on square root factorization. Numerical results on the accuracy and model reduction efficiency show attractive performance of the proposed method.