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Approximation of interacting kernels by sum of Gaussians (SOG) is frequentlyrequired in many applications of scientific and engineering computing in orderto construct efficient algorithms for kernel summation or convolution problems.In this paper, we propose a kernel-independent SOG method by introducing the dela Vall\'ee-Poussin sum and Chebyshev polynomials. The SOG works for generalinteracting kernels and the lower bound of Gaussian bandwidths is tunable andthus the Gaussians can be easily summed by fast Gaussian algorithms. The numberof Gaussians can be further reduced via the model reduction based on thebalanced truncation based on the square root method. Numerical results on theaccuracy and model reduction efficiency show attractive performance of theproposed method.

A kernel-independent sum-of-Gaussians method by de la Vall\'ee-Poussin sums