den Iseger, Peter Numerical transform inversion using Gaussian quadrature. (English) Zbl 1095.65116 Probab. Eng. Inf. Sci. 20, No. 1, 1-44 (2006). The author presents a simple Laplace transform inversion algorithm that can be 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, the location of these discontinuties and singularities are not known to us a priori. The algorithm only needs numerical values of the Laplace transform, is extremly fast, and the results are almost machine precision. The accuracy and robustness of the algorithm, are illustrated with various numerical examples. Reviewer: Som Prakash Goyal (Jaipur) Cited in 1 ReviewCited in 39 Documents MSC: 65R10 Numerical methods for integral transforms 44A10 Laplace transform Keywords:numerical inversion; Laplace transform; Gaussian quadrature; algorithm; functions with discontinuities and singularities; numerical examples Software:MCQueue; Algorithm 682 PDFBibTeX XMLCite \textit{P. den Iseger}, Probab. Eng. Inf. Sci. 20, No. 1, 1--44 (2006; Zbl 1095.65116) Full Text: DOI References: [1] DOI: 10.1145/361953.361969 · doi:10.1145/361953.361969 [2] Talbot, Journal of the Institute of Mathematics and Its Applications 23 pp 97– (1979) [3] Choudhury, Annals of Applied Probability 4 pp 719– (1994) [4] Carr, Journal of Computational Finance 2 pp 61– (1999) · doi:10.21314/JCF.1999.043 [5] DOI: 10.1137/1033097 · Zbl 0734.65104 · doi:10.1137/1033097 [6] Abate, ORSA Journal on Computing 7 pp 36– (1995) · Zbl 0821.65085 · doi:10.1287/ijoc.7.1.36 [7] DOI: 10.1007/BF01158520 · Zbl 0749.60013 · doi:10.1007/BF01158520 [8] DOI: 10.1016/0167-6377(92)90050-D · Zbl 0758.60014 · doi:10.1016/0167-6377(92)90050-D [9] DOI: 10.1016/S0166-5316(97)00002-3 · doi:10.1016/S0166-5316(97)00002-3 [10] Abate, INFORMS Journal on Computing 8 pp 413– (1996) [11] DOI: 10.1093/comjnl/14.4.433 · Zbl 0227.65019 · doi:10.1093/comjnl/14.4.433 [12] DOI: 10.1007/BF01535429 · Zbl 0263.65032 · doi:10.1007/BF01535429 [13] O’Cinneide, Stochastic Models 13 pp 315– (1997) [14] DOI: 10.1145/78928.78932 · Zbl 0900.65374 · doi:10.1145/78928.78932 [15] Gaver, Operations Research 14 pp 444– (1966) [16] DOI: 10.1145/321439.321446 · Zbl 0165.51403 · doi:10.1145/321439.321446 [17] DOI: 10.1016/0021-9991(79)90025-1 · Zbl 0416.65077 · doi:10.1016/0021-9991(79)90025-1 [18] DOI: 10.2307/2003354 · Zbl 0127.09002 · doi:10.2307/2003354 [19] DOI: 10.1145/321341.321351 · Zbl 0141.33401 · doi:10.1145/321341.321351 [20] DOI: 10.1239/aap/1086957588 · Zbl 1064.65151 · doi:10.1239/aap/1086957588 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.