li ~ - ItOUAND Recursive Pseudo-Inversion of the Laplace Transform on the Real Line Nassar H. S. Haidar Departments of Mathematics and Physics American University of Beirut, Lebanon P.O. Box 3085 850 Third Avenue, 18th Floor New York, NY 10022 ABSTRACT We develop the double series inverse Laplace transform, advanced by N. H. S. Haidar [1] into a recursive pseudo-inverse. This development is also based on real axis numerical data but iterates over both the real and complex domains through a recursive regularization algorithm. © Elsevier Science Inc., 1997 1. INTRODUCTION The numerical inversion of the Laplace transform F(s) =.9:{ f(t)} = fo e-'t f(t) dt (1.1) on the real line of the complex ( s = v + i~-)-plane is a well known example of severely ill-posed problems. This problem has been studied or addressed in a number of works in the past [2-6]. More recently, new methods have been proposed [1, 7, 8]. In [1] the author derived an inversion formula Which is based on the double series solution to Fredholm integral equations of the first-kind with nondegenerate kernels. The aim of this paper is to develop the real axis inversion method outlined in [1] into a recursive pseudo-inverse Laplace transform that is iterative over both the real and complex domains in a way interpolating between the data points of both the image and its preimage. APPLIED MA THEMA TICSAND COMPUTATION 84:213-220 (1997) © Elsevier ScienceInc., 1997 0096-3003/97/$17.00 655 Avenue of the Americas, New York, NY 10010 PII S0096-3003(96)00087-2