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.
|Advisor:||Sameh, Ahmed, Xia, Jianlin|
|Commitee:||Cai, Zhiqiang, Lucier, Bradley, Sameh, Ahmed, Xia, Jianlin|
|School Location:||United States -- Indiana|
|Source:||DAI-B 75/06(E), Dissertation Abstracts International|
|Subjects:||Mathematics, Computer science|
|Keywords:||Fiedler, Flexible generalized minimum residual algorithm, Nested convergence, Recursive projection method, generalized minimum residual algorithm|
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