A Kernel-Independent Sum-of-Exponentials Method

We propose an accurate algorithm for a novel sum-of-exponentials (SOE) approximation of kernel functions, and develop fast convolution quadrature based on the SOE, which allows order N calculation time steps approximating continuous temporal integral. The SOE method is constructed by combination de la Vallée-Poussin sum semi-analytical exponential expansion general kernel, model reduction technique to minimize number exponentials under given error tolerance. employ finite part splitting so that integral can be solved as system ordinary differential equations. show works kernels with controllable upperbound positive exponents. Numerical analysis provided both SOE-based quadrature. results different demonstrate attractive performance accuracy efficiency proposed method.