An Inversion Technique for the Laplace Transform

The purpose of this paper is to summarize the techniques presented in the paper "An Inversion Technique for the Laplace Transform" 1 and to make available a useful reference of properties of the 'approximation sequence,' and a new numerical method developed since the publication of Ref. 1. The inversion, or approximation sequence, retains the essential structural characteristics of the original function, e.g., nonnegativity, monotonicity, and convexity. Thus, we approximate a distribution function by distribution functions. For application to queueing theory, this may be considered quite important. The basic inversion sequence, together with error estimates, is discussed in Section II; also, two enhancement procedures are given-- namely, the construction of a sequence that is more rapidly convergent than the approximation sequence and which was not given in Ref. 1, and a method of accurate approximation to functions that decay exponentially. Section III discusses the new numerical method, and Section IV presents two examples of numerical inversion along with controls. Except for the new material whose derivations are given here, all proofs can be found in Ref. 1. 1995