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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Imberti, David Michael"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Ahmed Sameh","Jianlin Xia","Zhiqiang Cai","Bradley Lucier"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-10-01T07:00:00Z","date_published":"2013-10-01T07:00:00Z","updated_at":"2026-07-24T03:53:02Z","subjects":["pure sciences","applied sciences","flexible generalized minimum residual algorithm","fiedler","generalized minimum residual algorithm","nested convergence","recursive projection method","Computer Sciences","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://docs.lib.purdue.edu/open_access_dissertations/127","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ahmed Sameh","Jianlin Xia","Zhiqiang Cai","Bradley Lucier"]},{"key":"dc:creator","label":"Author","values":["Imberti, David Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["pure sciences","applied sciences","flexible generalized minimum residual algorithm","fiedler","generalized minimum residual algorithm","nested convergence","recursive projection method","Computer Sciences","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://docs.lib.purdue.edu/open_access_dissertations/127"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Methods For Increasing Domains Of Convergence In Iterative Linear System Solvers"]}]}],"canonical_facts":{"dc:contributor":["Ahmed Sameh","Jianlin Xia","Zhiqiang Cai","Bradley Lucier"],"dc:creator":["Imberti, David Michael"],"dc:description.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.
"],"dc:identifier":["https://docs.lib.purdue.edu/open_access_dissertations/127"],"dc:subject":["pure sciences","applied sciences","flexible generalized minimum residual algorithm","fiedler","generalized minimum residual algorithm","nested convergence","recursive projection method","Computer Sciences","Mathematics"],"dc:title":["Methods For Increasing Domains Of Convergence In Iterative Linear System Solvers"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:53:02Z"}