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

dc.contributor.authorLamm, Patricia K.en_US
dc.contributor.authorScofield, Thomas L.en_US
dc.date.accessioned2006-12-19T19:14:51Z
dc.date.available2006-12-19T19:14:51Z
dc.date.issued2000-04-01en_US
dc.identifier.citationLamm, Patricia K; Scofield, Thomas L (2000). "Sequential predictor-corrector methods for the variable regularization of Volterra inverse problems." Inverse Problems. 16(2): 373-399. <http://hdl.handle.net/2027.42/49104>en_US
dc.identifier.issn0266-5611en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/49104
dc.description.abstractWe 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.extent3118 bytes
dc.format.extent718188 bytes
dc.format.mimetypetext/plain
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherIOP Publishing Ltden_US
dc.titleSequential predictor-corrector methods for the variable regularization of Volterra inverse problemsen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationotherDepartment of Mathematics, Michigan State University, E Lansing, MI 48824-1027, USAen_US
dc.contributor.affiliationotherDepartment of Mathematics, University of Michigan-Flint, Flint, MI 48502-1950, USAen_US
dc.contributor.affiliationumcampusFlinten_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/49104/2/ip0208.pdfen_US
dc.identifier.doihttp://dx.doi.org/10.1088/0266-5611/16/2/308en_US
dc.identifier.sourceInverse Problems.en_US
dc.owningcollnameInterdisciplinary and Peer-Reviewed


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