On the Numerical Approximation of the Laplace Transform Function from Real Samples and Its Inversion

R. Campagna (), L. D’Amore (), A. Galletti (), A. Murli () and M. Rizzardi ()
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R. Campagna: University of Naples Federico II, Complesso Universitario M.S. Angelo
L. D’Amore: University of Naples Federico II, Complesso Universitario M.S. Angelo
A. Galletti: University of Naples Parthenope, Centro Direzionale
A. Murli: University of Naples Federico II, Complesso Universitario M.S. Angelo
M. Rizzardi: University of Naples Parthenope, Centro Direzionale

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 209-216 from Springer

Abstract: Abstract Many applications are tackled using the Laplace Transform (LT) known on a countable number of real values [J. Electroanal. Chem. 608, 37–46 (2007), Int. J. solid Struct. 41, 3653–3674 (2004), Imaging 26, 1183–1196 (2008), J. Magn. Reson. 156, 213–221 (2002)]. The usual approach to solve the LT inverse problem relies on a regularization technique combined with information a priori both on the LT function and on its inverse (see for instance [http://s-provencher.com/pages/ contin.shtml]). We propose a fitting model enjoying LT properties: we define a generalized spline that interpolates the LT function values and mimics the asymptotic behavior of LT functions. Then, we prove existence and uniqueness of this model and, through a suitable error analysis, we give a priori approximation error bounds to confirm the reliability of this approach. Numerical results are presented.

Date: 2010
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DOI: 10.1007/978-3-642-11795-4_21

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