1. On the Numerical Approximation of the Laplace Transform Function from Real Samples and Its Inversion
- Author
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Luisa D'Amore, Mariarosaria Rizzardi, Rosanna Campagna, Ardelio Galletti, Almerico Murli, Kreiss, G, Lotstedt, P, Malqvist, A, Neytcheva, M, Campagna, R, D'Amore, L, Galletti, A, Murli, A, Rizzardi, M, Gunilla Kreiss, Per Lötstedt, Axel Målqvist and Maya Neytcheva, Campagna, R., D'Amore, Luisa, Galletti, A., Murli, Almerico, and Rizzardi, M.
- Subjects
Spline (mathematics) ,Laplace transform ,Approximation error ,Mathematical analysis ,A priori and a posteriori ,Countable set ,Inverse ,Uniqueness ,Inverse problem ,Mathematics - 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.
- Published
- 2010