Numerical realization of piecewise-uniform regularization algorithms

An algorithm is considered for piecewise-uniform regularization of ill-posed problems with discontinuous solutions. It is based on the minimization of a Tikhonov functional of special type on a class of functions with bounded variation, with regularization parameter chosen according to the generaliz...

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Bibliographic Details
Published in:U.S.S.R. computational mathematics and mathematical physics 1987, Vol.27 (5), p.88-91
Main Author: Leonov, A.S.
Format: Article
Language:English
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Summary:An algorithm is considered for piecewise-uniform regularization of ill-posed problems with discontinuous solutions. It is based on the minimization of a Tikhonov functional of special type on a class of functions with bounded variation, with regularization parameter chosen according to the generalized residue principle. A minimization alglrithm is proposed whose effectiveness is confirmed by model calculations for the solution of first-order integral equations with discontinuous solutions.
ISSN:0041-5553
DOI:10.1016/0041-5553(87)90050-4