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

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • 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)

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.

Suggested Citation

  • R. Campagna & L. D’Amore & A. Galletti & A. Murli & M. Rizzardi, 2010. "On the Numerical Approximation of the Laplace Transform Function from Real Samples and Its Inversion," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 209-216, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_21
    DOI: 10.1007/978-3-642-11795-4_21
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