Date of Award

Fall 12-18-2014

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Alexandra Smirnova, PhD

Abstract

In the case of a linear ill-posed problem with noisy data, a version of an a posteriori parameter selection discrepancy principle (DP) is justified for an arbitrary regularization strategy under very general assumptions on the operator and the stabilizer. Its efficiency is demonstrated for a practically important inverse problem in avian influenza. We refer to our result as an abstract discrepancy principle (ADP), which shows that applicability of the DP largely depends on the level of noise in the data rather than the method used for the construction of a specific regularization procedure.

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