{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86876"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86876","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Particle Spreading in a Simple Majda Flow and Eigenvalue Estimation Through a Cayley Transform","abstract":"The spectrum of the integral operator whose kernel is the covariance function of a random variable plays an important role in finding the distribution of the random variable. We consider methods for producing estimates of the eigenvalues of such operators. If such an operator can be written in the form H0 + H1 with H 1 relatively compact to H0, then the eigenvalues are asymptotically close to those of H0. This method does not, however, produce good error estimates. We consider a perturbation method based on a Cayley transform. We show that the change of basis V = (I + K/2)-1( I - K/2), where I is the identity operator and K is a skew-adjoint operator given by a formal perturbation argument, gives better error estimate.","abstract_html":"The spectrum of the integral operator whose kernel is the covariance function of a random variable plays an important role in finding the distribution of the random variable. We consider methods for producing estimates of the eigenvalues of such operators. If such an operator can be written in the form H0 + H1 with H 1 relatively compact to H0, then the eigenvalues are asymptotically close to those of H0. This method does not, however, produce good error estimates. We consider a perturbation method based on a Cayley transform. We show that the change of basis V = (I + K/2)-1( I - K/2), where I is the identity operator and K is a skew-adjoint operator given by a formal perturbation argument, gives better error estimate.","abstract_has_math":false,"creators":["Lee, Jae-Ug"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Bronski, Jared C."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:19:58Z","date_published":"2015-09-28T15:19:58Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3250276"],"render_values":[{"text":"(MiAaPQ)AAI3250276","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86876","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Bronski, Jared C."]},{"key":"dc:creator","label":"Author","values":["Lee, Jae-Ug"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:19:58Z","10000-01-01","2006"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"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":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86876","(MiAaPQ)AAI3250276"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The spectrum of the integral operator whose kernel is the covariance function of a random variable plays an important role in finding the distribution of the random variable. We consider methods for producing estimates of the eigenvalues of such operators. If such an operator can be written in the form H0 + H1 with H 1 relatively compact to H0, then the eigenvalues are asymptotically close to those of H0. This method does not, however, produce good error estimates. We consider a perturbation method based on a Cayley transform. We show that the change of basis V = (I + K/2)-1( I - K/2), where I is the identity operator and K is a skew-adjoint operator given by a formal perturbation argument, gives better error estimate.","Made available in DSpace on 2015-09-28T15:19:58Z (GMT). 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We consider methods for producing estimates of the eigenvalues of such operators. If such an operator can be written in the form H0 + H1 with H 1 relatively compact to H0, then the eigenvalues are asymptotically close to those of H0. This method does not, however, produce good error estimates. We consider a perturbation method based on a Cayley transform. We show that the change of basis V = (I + K/2)-1( I - K/2), where I is the identity operator and K is a skew-adjoint operator given by a formal perturbation argument, gives better error estimate.","Made available in DSpace on 2015-09-28T15:19:58Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3250276.pdf: 1879937 bytes, checksum: 043fb409b7528aeab963468d5d9b17e3 (MD5) Previous issue date: 2006","Embargo set by: Seth Robbins for item 88157 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","66 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006."],"dc:identifier":["http://hdl.handle.net/2142/86876","(MiAaPQ)AAI3250276"],"dc:language":["eng"],"dc:subject":["Mathematics"],"dc:title":["Particle Spreading in a Simple Majda Flow and Eigenvalue Estimation Through a Cayley Transform"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:28Z"}