![]() ![]() Hansen, P.C.: Rank-deficient and discrete ill posed problems. Hanke, M., Scherzer, O.: Inverse problems light: numerical differentiation. Pitman Advanced publishing Program, Edinburgh (1990) Groetsch, C.W.: The theory of tikhonov regularization for fredholm equations of the first kind. ![]() (ed.) Numerical and applied mathematics, pp. Giunta, G., Murli, A.: An algorithm for inverting the Laplace transform using real and real sampled function values. Garbow, S., Giunta, G., Lyness, N.J., Murli, A.: Algorithm 662: a fortran software package for the numerical inversion of a Laplace transform based on week’s method. 33, 1–32 (1979)ĭemmel, J.: The probability that a numerical analysis problem is difficult. Kluwer Academic Publisher, Netherlands (2000)ĭavies, B., Martin, D.: Numerical inversion of Laplace transform. Reliadiff.: A C++ software package for Laplace transform Inversion, ACM Transaction on Mathematical Software, (in press).Įngl, H.W., Hanke, M., Neubauer, A.: Regularization of inverse problems. 63, 187–211 (2013)ĭ’Amore, L., Mele, V., Murli, A.: Performance analysis of the Taylor expansion coefficients computation as implemented by the software package TADIFF. An Ansi C90 software package for the real Laplace transform inversion. 210, 84–98 (2007)ĭ’Amore, L., Campagna, R., Galletti, A., Marcellino, L., Murli, A.: A smoothing spline that approximates Laplace transform functions only known on measurements on the real axis. Inverse Problems 18, 1185–1205 (2002)ĭ’Amore, L., Campagna, R., Murli, A.: An efficient algorithm for regularization of Laplace transform inversion in real case. Inverse Problems 16, 1441–1456 (2000)ĭ’Amore, L., Murli, A.: Regularization of a fourier series based method for the Laplace transform inversion in the real case. 25, 306–315 (1999)ĭ’Amore, L., Murli, A., Rizzardi, M.: An extension of the Henrici formula for Laplace transform inversion. 25, 279–305 (1999)ĭ’Amore, L., Laccetti, G., Murli, A.: Algorithm 796: a fortran software package for the numerical inversion of the Laplace transform based on a fourier series method. Springer, Berlin (2007)ĭ’Amore, L., Laccetti, G., Murli, A.: An implementation of a Fourier series method for the numerical inversion of the Laplace transform. 8, 254–265 (1971)Ĭohen, A.M.: Numerical methods for Laplace transform inversion. Springer, Berlin (2008)Ĭullum, J.: Numerical differentiation and regularization, SIAM. (eds.) Advances in automatic differentiation, pp. In: Bischof, C.H., Bücker, H.M., Hovland, P.D., Naumann, U., Utke, J. 198, 98–115 (2007)Ĭuomo, S., D’Amore, L., Murli, A., Rizzardi, M.: A Modification of Weeks’ Method for numerical inversion of the Laplace transform in the real case based on automatic differentiation. Inverse Problems 7, 21–41 (1991)Ĭuomo, S., D’Amore, L., Murli, A., Rizzardi, M.: Computation of the inverse Laplace transform based on a collocation method which uses only real values. Elsevier, Amsterdam (1966)īertero, M., Pike, E.R.: Exponential-sampling method for Laplace and other dilationally invariant transforms: I. Sinc filter – ideal sinc filter (aka rectangular filter) is acausal and has an infinite delay.Bellman, R., Kalaba, R., Lockett, J.A.: Numerical inversion of the Laplace transform: applications to biology, economics, engineering, and physics.If f( t) is a real- or complex-valued function of the real variable t defined for all real numbers, then the two-sided Laplace transform is defined by the integralī Two-sided Laplace transforms are closely related to the Fourier transform, the Mellin transform, the Z-transform and the ordinary or one-sided Laplace transform. In mathematics, the two-sided Laplace transform or bilateral Laplace transform is an integral transform equivalent to probability's moment generating function. ( September 2015) ( Learn how and when to remove this template message) Please help to improve this article by introducing more precise citations. This article includes a list of general references, but it lacks sufficient corresponding inline citations. ![]()
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