Diffusive representation of pseudo-differential operators is a theory that has attracted interest during the last years, and the discretization of the diffusive representation allows significant simplifications for numerical integration encountered in many physical models. The feasibility of such integration relies on efficient determination of the coefficients involved in the representation. In this report a novel way to determine such coefficients is proposed based on non-linear optimization. Compared to the typical method using Gaussian quadrature, our new approach is shown to lead to more accurate approximation in a particular case with application to computational biology.
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