NUMERICAL INVERSION OF MULTIDIMENSIONAL LAPLACE TRANSFORMS BY THE LAGUERRE METHOD

Numerical transform inversion can be useful to solve stochastic models arising in the performance evaluation of telecommunications and compu ter systems. We contribute to this technique in this paper by extendin g our recently developed variant of the Laguerre method for numericall y inverting Laplace transforms to multidimensional Laplace transforms. An important application of multidimensional inversion is to calculat e time-dependent performance measures of stochastic systems. Key featu res of our new algorithm are: (1) an efficient FFT-based extension of our previously developed variant of the Fourier-series method to calcu late the coefficients of the multidimensional Laguerre generating func tion, and (2) systematic methods for scaling to accelerate convergence of infinite series, using Wynn's epsilon-algorithm and exploiting geo metric decay rates of Laguerre coefficients, These features greatly sp eed up the algorithm while controlling errors. We illustrate the effec tiveness of our algorithm through numerical examples. For many problem s, hundreds of function evaluations can be computed in just a few seco nds. (C) 1998 Published by Elsevier Science B.V.