# Sequential predictor-corrector methods for the variable regularization of Volterra inverse problems

 dc.contributor.author Lamm, Patricia K. en_US dc.contributor.author Scofield, Thomas L. en_US dc.date.accessioned 2006-12-19T19:14:51Z dc.date.available 2006-12-19T19:14:51Z dc.date.issued 2000-04-01 en_US dc.identifier.citation Lamm, Patricia K; Scofield, Thomas L (2000). "Sequential predictor-corrector methods for the variable regularization of Volterra inverse problems." Inverse Problems. 16(2): 373-399. en_US dc.identifier.issn 0266-5611 en_US dc.identifier.uri https://hdl.handle.net/2027.42/49104 dc.description.abstract We analyse the convergence of a class of discrete predictor-corrector methods for the sequential regularization of first-kind Volterra integral equations. In contrast to classical methods such as Tikhonov regularization, this class of methods preserves the Volterra (causal) structure of the original problem. The result is a discretized regularization method for which the number of arithmetic operations is (N 2 ) (where N is the dimension of the approximating space) in contrast to standard Tikhonov regularization which requires (N 3 ) operations. In addition, the method considered here is defined using functional regularization parameters so that the possibility for more or less smoothing at different points in the domain of the solution is allowed. We establish a convergence theory for these methods and present relevant numerical examples, illustrating how one functional regularization parameter may be adaptively selected as part of the sequential regularization process. This work generalizes earlier results by the first author to the case of a penalized predictor-corrector formulation, functional regularization parameters, and nonconvolution Volterra equations. en_US dc.format.extent 3118 bytes dc.format.extent 718188 bytes dc.format.mimetype text/plain dc.format.mimetype application/pdf dc.language.iso en_US dc.publisher IOP Publishing Ltd en_US dc.title Sequential predictor-corrector methods for the variable regularization of Volterra inverse problems en_US dc.type Article en_US dc.subject.hlbsecondlevel Physics en_US dc.subject.hlbtoplevel Science en_US dc.description.peerreviewed Peer Reviewed en_US dc.contributor.affiliationother Department of Mathematics, Michigan State University, E Lansing, MI 48824-1027, USA en_US dc.contributor.affiliationother Department of Mathematics, University of Michigan-Flint, Flint, MI 48502-1950, USA en_US dc.contributor.affiliationumcampus Flint en_US dc.description.bitstreamurl http://deepblue.lib.umich.edu/bitstream/2027.42/49104/2/ip0208.pdf en_US dc.identifier.doi http://dx.doi.org/10.1088/0266-5611/16/2/308 en_US dc.identifier.source Inverse Problems. en_US dc.owningcollname Interdisciplinary and Peer-Reviewed
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