  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 Vall\'ee-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.
