Date of Award

Fall 2013

Degree Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Ahmed Sameh

Second Advisor

Jianlin Xia

Committee Chair

Ahmed Sameh

Committee Member 1

Jianlin Xia

Committee Member 2

Zhiqiang Cai

Committee Member 3

Bradley Lucier


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.