Fast Algorithm for the Discrete Laplace Transformation

摘要

An algorithm is presented for the rapid evaluation of expressions of the form sum over j = 1 to m of (a sub j) exp (- beta sub j )x) at multiple points x1, x2, ..., xn. In order to evaluate the above sum at n points, the algorithm requires order O(n + m) operations, and a simple modification of the scheme provides an order O(n) procedure for the evaluation of an order n polynomial at n arbitrary real points. The algorithm is numerically stable, and its practical usefulness is demonstrated by numerical examples.