An analysis of bilinear transform polynomial methods of inversion of Laplace transforms

Summary.

Methods for the numerical inversion of a Laplace transform$F(s)$ which use a special bilinear transformation of $s$ are particularly effective in many cases and are widely used. The main purpose of this paper is to analyze the convergence and conditioning properties of a special class of such methods, characterized by the use of Lagrange interpolation. The results derived apply both to complex and real inversion, and show that some known inversion methods are in fact in this class.