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dc.contributor.advisorGeorge, Santhosh-
dc.contributor.authorSreedeep, C. D.-
dc.date.accessioned2020-09-18T10:30:06Z-
dc.date.available2020-09-18T10:30:06Z-
dc.date.issued2019-
dc.identifier.urihttp://idr.nitk.ac.in/jspui/handle/123456789/14526-
dc.description.abstractIn science and engineering many practical problems can be formulated using mathematical modelling and can be classified as nonlinear ill-posed problems. Here we consider those ill-posed equations involving m-accretive operators in Banach spaces. Using a general H¨older type source condition we were able to obtain an optimal order error estimate. For nonlinear problems, obtaining a closed form solution is possible only in rare cases, so most of the methods considered for approximating the solution of nonlinear problems are iterative. Four different types of iterative schemes are being discussed in this thesis. Firstly, we consider a derivative and inverse free method and obtained second order convergence. Then, we produced an extended Newton-type iterative scheme that converges cubically to the solution which uses assumptions only on the first Fr´echet derivative of the operator. Afterwards, we studied Newton-Kantorovich regularization method and obtained second order convergence with weak assumptions. Finally, we examined Secant-type iteration and proved that the proposed iterative scheme has a convergence order at least 2.20557 using assumptions only on first Fr´echet derivative of the operator. Through out the work, for choosing the regularization parameter we have taken the adaptive parameter choice strategy given by Pereverzev and Schock (2005).en_US
dc.language.isoenen_US
dc.publisherNational Institute of Technology Karnataka, Surathkalen_US
dc.subjectDepartment of Mathematical and Computational Sciencesen_US
dc.subjectBanach spaceen_US
dc.subjectNonlinear ill-posed problemen_US
dc.subjectLavrentiev regularizationen_US
dc.subjectm-accretive mappingsen_US
dc.subjectAdaptive parameter choice strategyen_US
dc.subjectExtended Newton iterative schemeen_US
dc.subjectNewton-Kantorovich regularization methoden_US
dc.subjectSecant-type iterative schemeen_US
dc.titleIterative Regularization Theory for Nonlinear Ill-Posed Problemsen_US
dc.typeThesisen_US
Appears in Collections:1. Ph.D Theses

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