caa a22 4500 378866532 CHVBK 20180305123359.0 cr unu---uuuuu 161128e20030901xx s 000 0 eng 10.1515/156939403769237051 doi (NATIONALLICENCE)gruyter-10.1515/156939403769237051 Schuster T. Fachbereich Mathematik, Geb. 36, Universität des Saarlandes, 66041 Saarbrücken, Germany. E-mail: thomas.schuster@num.uni-sb.de A stable inversion scheme for the Laplace transform using arbitrarily distributed data scanning points [Elektronische Daten] [T. Schuster] In many industrial applications inversion of the Laplace transform is necessary to reconstruct a searched for object function. In X-ray diffractometry, a method from non-destructive testing, we want to recover the stress tensor of a specimen with the help of X-ray measurements. The mathematical model is described by the Laplace transform of the stress tensor at finitely many scanning points that are not equally distributed. In this article we present an inversion method for the Laplace transform using a non-equispaced sampling grid that applies the approximate inverse to this transform. The approximate inverse is a regularization technique for inverse problems based on evaluations 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 dilation invariant mollifiers, which are designed particularly for this operator. An error estimate is given and point-wise convergence of the approximate inverse to the exact solution is proved. The paper ends with some numerical results. Copyright 2003, Walter de Gruyter Journal of Inverse and Ill-posed Problems Walter de Gruyter 11/3(2003-09-01), 263-287 0928-0219 11:3<263 2003 11 jiip https://doi.org/10.1515/156939403769237051 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/156939403769237051 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Schuster T. Fachbereich Mathematik, Geb. 36, Universität des Saarlandes, 66041 Saarbrücken, Germany. E-mail: thomas.schuster@num.uni-sb.de NATIONALLICENCE 773 0- Journal of Inverse and Ill-posed Problems Walter de Gruyter 11/3(2003-09-01), 263-287 0928-0219 11:3<263 2003 11 jiip CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter