Dempster–Shafer evidential theory for the automated selection of parameters for Talbot’s method contours and application to matrix exponentiation

In this paper, the Dempster–Shafer theory of evidential reasoning is applied to the problem of optimal contour parameters selection in Talbot’s method for the numerical inversion of the Laplace transform. The fundamental concept is the discrimination between rules for the parameters that define the shape of the contour based on the features of the function to invert. To demonstrate the approach, it is applied to the computation of the matrix exponential via numerical inversion of the corresponding resolvent matrix. Training for the Dempster–Shafer approach is performed on random matrices. The algorithms presented have been implemented in MATLAB. The approximated exponentials from the algorithm are compared with those from the rational approximation for the matrix exponential returned by the MATLAB expm function.