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A novel mollifier inversion scheme for the Laplace transform
Author(s) -
Schuster T.
Publication year - 2002
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/1617-7061(200203)1:1<422::aid-pamm422>3.0.co;2-n
Subject(s) - inverse laplace transform , laplace transform , two sided laplace transform , equidistant , laplace transform applied to differential equations , post's inversion formula , inversion (geology) , laplace–stieltjes transform , mathematics , mellin transform , regularization (linguistics) , inverse , mellin inversion theorem , inverse problem , kernel (algebra) , green's function for the three variable laplace equation , scalar (mathematics) , algorithm , mathematical analysis , computer science , fourier transform , artificial intelligence , geometry , fractional fourier transform , discrete mathematics , structural basin , fourier analysis , paleontology , biology
In this article we present a novel inversion method for the Laplace transform for non‐equidistant scanning points applying the approximate inverse to this transform. The approximate inverse is a regularization technique for inverse problems based on evaluations of scalar products of the given data with so called reconstruction kernels. Each kernel solves a system of linear equations defined by the adjoint of the Laplace transform and dilatation invariant mollifiers, which are designed articularly for this operator. The paper includes numerical results.