Numerical solutions of linear ill-posed problems

In this paper, a method is described for inverting the Mellin transform which uses an expansion in Laguerre polynomials and converts Mellin transform to Laplace transform, then a regularization method is used to recover the original function of the Mellin transform. The performance of the method is...

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Bibliographic Details
Published in:Integral transforms and special functions Vol. 16; no. 1; pp. 29 - 37
Main Author: Iqbal, M.
Format: Journal Article
Language:English
Published: Taylor & Francis 01.01.2005
Subjects:
Convergence
Cross-validation method
Filter function
Ill-posed problems
Influence matrix
Laguerre polynomials
Mellin transform
Regularization
Stabilizing functional
ISSN:1065-2469, 1476-8291
Online Access:Get full text
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Summary:In this paper, a method is described for inverting the Mellin transform which uses an expansion in Laguerre polynomials and converts Mellin transform to Laplace transform, then a regularization method is used to recover the original function of the Mellin transform. The performance of the method is illustrated by the inversion of the test functions available in the literature. Results are shown in the table.
ISSN:1065-2469
1476-8291
DOI:10.1080/1065246042000271992