Methods for increasing domains of convergence in iterative linear system solvers

• Main Author: Imberti, David M.
• Language: EN
• Published: Purdue University 2014
• Subjects: Mathematics|Computer Science
• Online Access: http://pqdtopen.proquest.com/#viewpdf?dispub=3613148

<p> 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.</p>