%0 Journal Article %1 dehoog1982improved %A de Hoog, F. R. %A Knight, J. H. %A Stokes, A. N. %D 1982 %J SIAM J. Sci. Statist. Comput. %K Laplace_inversion Pade_approximation continued_fractions inverse_problems %N 3 %P 357--366 %R 10.1137/0903022 %T An improved method for numerical inversion of Laplace transforms %U http://dx.doi.org/10.1137/0903022 %V 3 %X An improved procedure for numerical inversion of Laplace transforms is proposed based on accelerating the convergence of the Fourier series obtained from the inversion integral using the trapezoidal rule. When the full complex series is used, at each time-value the epsilon-algorithm computes a .(trigonometric) Padé approximation which gives better results than existing acceleration methods. The quotient-difference algorithm is used to compute the coefficients of the corresponding continued fraction, which is evaluated at each time-value, greatly improving efficiency. The convergence of the continued fraction can in turn be accelerated, leading to a further improvement in accuracy. Note: code at http://www.cs.hs-rm.de/~weber/lapinv/dehoog/dehoog.htm and often cites Hollenbeck, who says: % algorithm: de Hoog et al's quotient difference method with accelerated % convergence for the continued fraction expansion % de Hoog, F. R., Knight, J. H., and Stokes, A. N. (1982). An improved % method for numerical inversion of Laplace transforms. S.I.A.M. J. Sci. % and Stat. Comput., 3, 357-366. % Modification: The time vector is split in segments of equal magnitude % which are inverted individually. This gives a better overall accuracy. % details: de Hoog et al's algorithm f4 with modifications (T->2*T and % introduction of tol). Corrected error in formulation of z.

@article{dehoog1982improved, abstract = {An improved procedure for numerical inversion of Laplace transforms is proposed based on accelerating the convergence of the Fourier series obtained from the inversion integral using the trapezoidal rule. When the full complex series is used, at each time-value the epsilon-algorithm computes a .(trigonometric) Padé approximation which gives better results than existing acceleration methods. The quotient-difference algorithm is used to compute the coefficients of the corresponding continued fraction, which is evaluated at each time-value, greatly improving efficiency. The convergence of the continued fraction can in turn be accelerated, leading to a further improvement in accuracy. Note: code at \url{http://www.cs.hs-rm.de/~weber/lapinv/dehoog/dehoog.htm} and often cites Hollenbeck, who says: % algorithm: de Hoog et al's quotient difference method with accelerated % convergence for the continued fraction expansion % [de Hoog, F. R., Knight, J. H., and Stokes, A. N. (1982). An improved % method for numerical inversion of Laplace transforms. S.I.A.M. J. Sci. % and Stat. Comput., 3, 357-366.] % Modification: The time vector is split in segments of equal magnitude % which are inverted individually. This gives a better overall accuracy. % details: de Hoog et al's algorithm f4 with modifications (T->2*T and % introduction of tol). Corrected error in formulation of z.}, added-at = {2012-07-15T22:32:56.000+0200}, author = {{de Hoog}, F. R. and Knight, J. H. and Stokes, A. N.}, biburl = {https://www.bibsonomy.org/bibtex/2be6e490ae48fa8a2fbc384369480f738/peter.ralph}, coden = {SIJCD4}, description = {An Improved Method for Numerical Inversion of Laplace Transforms}, doi = {10.1137/0903022}, fjournal = {Society for Industrial and Applied Mathematics. Journal on Scientific and Statistical Computing}, interhash = {c9ea1424bc8cbf1a9a9c1d0a145a5a52}, intrahash = {be6e490ae48fa8a2fbc384369480f738}, issn = {0196-5204}, journal = {SIAM J. Sci. Statist. Comput.}, keywords = {Laplace_inversion Pade_approximation continued_fractions inverse_problems}, mrclass = {65R10}, mrnumber = {667833 (84h:65113)}, number = 3, pages = {357--366}, timestamp = {2012-07-15T22:32:57.000+0200}, title = {An improved method for numerical inversion of {L}aplace transforms}, url = {http://dx.doi.org/10.1137/0903022}, volume = 3, year = 1982 }