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dc.contributor.advisorGeorge, Santhosh-
dc.contributor.authorM, Sabari-
dc.date.accessioned2020-06-25T04:50:53Z-
dc.date.available2020-06-25T04:50:53Z-
dc.date.issued2018-
dc.identifier.urihttp://idr.nitk.ac.in/jspui/handle/123456789/14125-
dc.description.abstractIn this thesis, we consider steepest descent method and minimal error method for approximating a solution of the nonlinear ill-posed operator equation F(x) = y, where F : D(F) ⊆ X → Y is nonlinear Fr´echet differentiable operator between the Hilbert spaces X and Y. In practical application, we have only noisy data yδ with ∥y − yδ∥ ≤ δ. To our knowledge, convergence rate result for the steepest descent method and minimal error method with noisy data are not known. We provide error estimate for these methods with noisy data. We modified these methods with less computational cost. Error estimate for steepest descent method and minimal error method is not known under H¨older-type source condition. We provide an error estimate for these methods under H¨older-type source condition and also with noisy data. We also studied the regularized version of steepest descent method and regularization parameter in this regularized version is selected through the adaptive scheme of 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.subjectIll-posed nonlinear equationsen_US
dc.subjectSteepest descent methoden_US
dc.subjectMinimal error methoden_US
dc.subjectRegularization methoden_US
dc.subjectTikhonov regularizationen_US
dc.subjectDiscrepancy principleen_US
dc.subjectBalancing principleen_US
dc.titleSteepest Descent Type Methods for Nonlinear Ill-Posed Operator Equationsen_US
dc.typeThesisen_US
Appears in Collections:1. Ph.D Theses

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