Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Algorithm 682: Talbot's method of the Laplace inversion problems
ACM Transactions on Mathematical Software (TOMS)
The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
Numerical inversion of multidimensional Laplace transforms by the Laguerre method
Performance Evaluation
Numerical Inversion of Laplace Transforms Using Laguerre Functions
Journal of the ACM (JACM)
Numerical Inversion of Laplace Transforms by Relating Them to the Finite Fourier Cosine Transform
Journal of the ACM (JACM)
Algorithm 368: Numerical inversion of Laplace transforms [D5]
Communications of the ACM
A Unified Framework for Numerically Inverting Laplace Transforms
INFORMS Journal on Computing
Sojourn Time Tails In The M/D/1 Processor Sharing Queue
Probability in the Engineering and Informational Sciences
Matrix-geometric algorithms for stochastic fluid flows
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Matrix-geometric algorithms for stochastic fluid flows
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Processor sharing: A survey of the mathematical theory
Automation and Remote Control
Renewal theory with exponential and hyperbolic discounting
Probability in the Engineering and Informational Sciences
Approximations for the M/GI/N+GI type call center
Queueing Systems: Theory and Applications
Numerical accuracy of real inversion formulas for the Laplace transform
Journal of Computational and Applied Mathematics
Traffic generated by a semi-markov additive process
Probability in the Engineering and Informational Sciences
Decoupled overlapping grids for the numerical modeling of oil wells
Journal of Computational Physics
On the infimum attained by a reflected Lévy process
Queueing Systems: Theory and Applications
A queueing system with batch arrival of customers in sessions
Computers and Industrial Engineering
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Numerical inversion of Laplace transforms is a powerful tool in computational probability. It greatly enhances the applicability of stochastic models in many fields. In this article we present a simple Laplace transform inversion algorithm that can compute the desired function values for a much larger class of Laplace transforms than the ones that can be inverted with the known methods in the literature. The algorithm can invert Laplace transforms of functions with discontinuities and singularities, even if we do not know the location of these discontinuities and singularities a priori. The algorithm only needs numerical values of the Laplace transform, is extremely fast, and the results are of almost machine precision. We also present a two-dimensional variant of the Laplace transform inversion algorithm. We illustrate the accuracy and robustness of the algorithms with various numerical examples.