Best rational function approximation to Laplace transform inversion using a window function

摘要

The best rational function approximation for Laplace transform inversion due to Longman is modified by the introduction of an appropriate “window” function. This window function enables one to approximate the inverse transform f(t) by a linear combination gn(t) of n exponential functions accurately in a given interval about a given point along the t-axis. It is proved that the sequence of approximants {gn(t)}n = 1∞ converges to f(t) in the mean. The method is illustrated by some numerical examples.