Abstract
In this thesis, we introduce and improve various methods for increasing the domains of convergence for iterative linear system solvers. We rely on the following three approaches: making the iteration adaptive, or nesting an inner iteration inside of a previously determined outer iteration; using deflation and projections to manipulate the spectra inherent to the iteration; and/or focusing on reordering schemes. We will analyze a specific combination of these three strategies. In particular, we propose to examine the influence of nesting a Flexible Generalized Minimum Residual algorithm together with an inner Recursive Projection Method using a banded preconditioner resulting from the Fiedler reordering.
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
Committee Chair
Ahmed Sameh
Date of Award
Fall 2013
Recommended Citation
Imberti, David Michael, "Methods For Increasing Domains Of Convergence In Iterative Linear System Solvers" (2013). Open Access Dissertations. 127.
https://docs.lib.purdue.edu/open_access_dissertations/127
First Advisor
Ahmed Sameh
Second Advisor
Jianlin Xia
Committee Member 1
Jianlin Xia
Committee Member 2
Zhiqiang Cai
Committee Member 3
Bradley Lucier