Date of Award
8-11-2015
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics and Statistics
First Advisor
Alexandra Smirnova
Second Advisor
Vladimir Bondarenko
Third Advisor
Zhongshan Li
Fourth Advisor
Michael Stewart
Abstract
Ill-posed inverse problems have wide applications in many fields such as oceanography, signal processing, machine learning, biomedical imaging, remote sensing, geophysics, and others. In this dissertation, we address the problem of solving unstable operator equations with iteratively regularized Newton-type algorithms. Important practical questions such as selection of regularization parameters, construction of generating (filtering) functions based on a priori information available for different models, algorithms for stopping rules and error estimates are investigated with equal attention given to theoretical study and numerical experiments.
DOI
https://doi.org/10.57709/7123282
Recommended Citation
Liu, Hui, "On Regularized Newton-type Algorithms and A Posteriori Error Estimates for Solving Ill-posed Inverse Problems." Dissertation, Georgia State University, 2015.
doi: https://doi.org/10.57709/7123282