A Unified Framework for Numerically Inverting Laplace Transforms
Published Online:1 Nov 2006https://doi.org/10.1287/ijoc.1050.0137
References
- Multi-precision Laplace inversion. Internat. J. Numer. Meth. Engrg. (2004) 60:979–993Crossref, Google Scholar
- The Fourier-series method for inverting transforms of probability distributions. Queueing Systems (1992) 10:5–88Crossref, Google Scholar
- Numerical inversion of Laplace transforms of probability distributions. ORSA J. Comput. (1995) 7:36–43Link, Google Scholar
- Asymptotics for M/G/1 low-priority waiting-time tail probabilities. Queueing Systems (1997) 25:173–223Crossref, Google Scholar
- Numerical inversion of multidimensional Laplace transforms by the Laguerre method. Performance Eval. (1998) 31:229–243Crossref, Google Scholar
- , Grassman W. An introduction to numerical inversion and its application to probability models. Computational Probability (1999) (Kluwer, Boston, MA) 257–323Google Scholar
- Power algorithms for inverting Laplace transforms. (2006) . Columbia University, New York. Available at http://www.columbia.edu/∼ww2040/recent.htmlGoogle Scholar
- Padé Approximants, 2nd ed. Encyclopedia of Mathematics and Its Applications (1996) 59(Cambridge University Press, Cambridge, UK) Google Scholar
- Regular Variation. Encyclopedia of Mathematics and Its Applications (1987) 27(Cambridge University Press, Cambridge, UK) Google Scholar
- Probabilistic scaling for the numerical inversion of nonprobability transforms. INFORMS J. Comput. (1997) 9:175–184Link, Google Scholar
- Calculating normalization constants of closed queueing networks by numerically inverting their generating functions. J. ACM (1995a) 42:935–970Crossref, Google Scholar
- An inversion algorithm to compute blocking probabilities in loss networks with state-dependent rates. IEEE/ACM Trans. Networking (1995b) 3:585–601Crossref, Google Scholar
- Multidimensional transform inversion with applications to the transient M/G/1 queue. Ann. Appl. Probab. (1994a) 4:719–740Crossref, Google Scholar
- The transient BMAP/G/1 queue. Stochastic Models (1994b) 10:145–182Crossref, Google Scholar
- Numerical solution of Mt/Gt/1 queues. Oper. Res. (1997) 45:451–463Link, Google Scholar
- Integral Transforms and Their Applications (2002) 3rd ed.(Springer, New York) Crossref, Google Scholar
- Numerical inversion of the Laplace transform: A survey and comparison of methods. J. Computational Phys. (1979) 33:1–32Crossref, Google Scholar
- Methods of Numerical Integration (1984) (Academic Press, New York) Google Scholar
- Operational Calculus in Two Variables and Applications (1962) (Pergamon, New York) . (English translation of 1958 Russian edition.)Google Scholar
- Introduction to the Theory and Application of the Laplace Transformation (1974) (Springer, New York) Crossref, Google Scholar
- Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform. J. ACM (1968) 15:115–123Crossref, Google Scholar
- On the numerical inversion of Laplace transforms: Comparison of three new methods on characteristic problems from applications. ACM Trans. Math. Software (1993) 19:333–359Crossref, Google Scholar
- Numerical inversion of Laplace transforms using optimal contours in the complex plane. Internat. J. Comput. Math. (1993) 49:93–105Crossref, Google Scholar
- Laplace transform inversion using optimal contours in the complex plane. Internat. J. Comput. Math. (2000) 73:531–543Crossref, Google Scholar
- An Introduction to Probability Theory and Its Applications (1971) 2nd ed.(Wiley, New York) Google Scholar
- Observing stochastic processes and approximate transform inversion. Oper. Res. (1966) 14:444–459Link, Google Scholar
- Applied Laplace Transforms and z-Transforms for Scientists and Engineers: A Computational Approach Using a Mathematica Package (2004) (Birkhauser-Verlag, Berlin, Germany) Crossref, Google Scholar
- Numerical inversion of 2-D Laplace transforms by fast Hartley transform computations. J. Franklin Inst. (1999) 336:955–972Crossref, Google Scholar
- An Introduction to Stochastic Processes (1997) (Duxbury Press, New York) Google Scholar
- Formulas and Theorems for the Special Functions of Mathematical Physics (1966) (Springer, New York) Crossref, Google Scholar
- Algorithm 682. Talbot’s method for the Laplace inversion problem. ACM Trans. Math. Software (1990) 16:158–168Crossref, Google Scholar
- Numerical operational methods for time-dependent linear problems. Internat. J. Numer. Methods Engrg. (1982) 18:1829–1854Crossref, Google Scholar
- Euler summation for Fourier series and Laplace transform inversion. Stochastic Models (1997) 13:315–337Crossref, Google Scholar
- New quadrature formulas for the numerical inversion of the Laplace transform. BIT (1969) 9:351–361Crossref, Google Scholar
- Gaussian quadrature formulas for the numerical inversion of the Laplace transform. J. Engrg. Math. (1971) 5:1–9Crossref, Google Scholar
- Numerical inversion of the Laplace transform of functions with discontinuities. Adv. Appl. Probab. (2004) 36:616–642Crossref, Google Scholar
- Algorithm 368: Numerical inversion of Laplace transforms. Comm. ACM (1970) 13:47–49, 624Crossref, Google Scholar
- The accurate inversion of Laplace transforms. J. Inst. Math. Appl. (1979) 23:97–120Crossref, Google Scholar
- Comparison of sequence accelerators for the Gaver method of numerical Laplace transform inversion. Comput. Math. Appl. (2004) 48:629–636Crossref, Google Scholar
- The List (2001) . Bibliography of papers on numerical transform inversion and its application. http://pumpjack.tamu.edu/∼valkoGoogle Scholar
- Numerical method for transient responses. J. Franklin Inst. (1969) 288:91–113Google Scholar
- Generalization of Vlach’s method for the numerical inversion of the Laplace transform. Electronic Lett. (1970) 6:742–744Crossref, Google Scholar
- Numerical inversion of Laplace transform. Electronic Lett. (1969) 5:120–121Crossref, Google Scholar
- Optimisation of numerical inversion of Laplace transforms. Electronic Lett. (1970) 6:677–679Crossref, Google Scholar
- , Graves-Morris P. R. Properties of IMN approximants. Padé Approximants and Their Applications (1973) (Academic Press, New York) 141–144Google Scholar

