Date of Award
12-2009
Degree Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
First Advisor
Dr. Alexandra Smirnova
Second Advisor
Dr. Michael Stewart
Third Advisor
Dr. Vladimir Bondarenko
Abstract
A concept of a well-posed problem was initially introduced by J. Hadamard in 1923, who expressed the idea that every mathematical model should have a unique solution, stable with respect to noise in the input data. If at least one of those properties is violated, the problem is ill-posed (and unstable). There are numerous examples of ill- posed problems in computational mathematics and applications. Classical numerical algorithms, when used for an ill-posed model, turn out to be divergent. Hence one has to develop special regularization techniques, which take advantage of an a priori information (normally available), in order to solve an ill-posed problem in a stable fashion. In this thesis, theoretical and numerical investigation of Tikhonov's (variational) regularization is presented. The regularization parameter is computed by the discrepancy principle of Morozov, and a first-kind integral equation is used for numerical simulations.
DOI
https://doi.org/10.57709/1234875
Recommended Citation
Whitney, MaryGeorge L., "Theoretical and Numerical Study of Tikhonov's Regularization and Morozov's Discrepancy Principle." Thesis, Georgia State University, 2009.
doi: https://doi.org/10.57709/1234875