{"id":{"repo_id":"regina","oai_identifier":"oai:uregina.scholaris.ca:10294/6862"},"canonical_url":"https://search.dev.ndltd.org/etd/regina/oai:uregina.scholaris.ca:10294/6862","repository":{"repo_id":"regina","name":"University of Regina","base_url":"https://uregina.scholaris.ca/server/oai/request"},"display":{"title":"Analysis and Numerical Methods for Algebraic Riccati Equations Associated with Regular M-Matrices","abstract":"The thesis is a further study about algebraic Riccati equations for which the four coe cient matrices form a regular M-matrix K. We prove a property about minimal nonnegative solutions of such an algebraic Riccati equation and its dual equation. And we show that Newton's method, SDA, ADDA are well-de ned and quadratically convergent in non-critical case. Then we prove that ADDA is linearly convergent with rate 1=2 in critical case. As compared to earlier work on solving regular MARE by ADDA, the results we present here are more general. This thesis extends the knowledge of doubling algorithms.","abstract_html":"The thesis is a further study about algebraic Riccati equations for which the four coe cient matrices form a regular M-matrix K. We prove a property about minimal nonnegative solutions of such an algebraic Riccati equation and its dual equation. And we show that Newton's method, SDA, ADDA are well-de ned and quadratically convergent in non-critical case. Then we prove that ADDA is linearly convergent with rate 1=2 in critical case. As compared to earlier work on solving regular MARE by ADDA, the results we present here are more general. This thesis extends the knowledge of doubling algorithms.","abstract_has_math":false,"creators":["Lu, Di"],"institution":"Faculty of Graduate Studies and Research, University of Regina","degree_name":"Master of Science (MSc)","degree_level":"Master's","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":["Guo, Chun-Hua"],"committee_chairs":[],"committee_members":["Argerami, Martin","Szechtman, Fernando"],"year":2015,"date_issued":"2015-12","date_published":"2015-12","updated_at":"2026-07-24T04:03:49Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4990"],"render_values":[{"text":"https://doi.org/10.82465/4990","href":"https://doi.org/10.82465/4990","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10294/6862","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Guo, Chun-Hua"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Argerami, Martin","Szechtman, Fernando"]},{"key":"dc:creator","label":"Author","values":["Lu, Di"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-07-27T19:59:22Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-07-27T19:59:22Z"]},{"key":"dc:date.issued","label":"Date","values":["2015-12"]},{"key":"dc:publisher","label":"Institution","values":["Faculty of Graduate Studies and Research, University of Regina"]},{"key":"dc:type","label":"Dc Type","values":["master thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Master's"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MSc)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Faculty of Graduate Studies and Research, University of Regina"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4990"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10294/6862"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Mathematics, University of Regina. iv, 56 p."]},{"key":"dc:description.abstract","label":"Abstract","values":["The thesis is a further study about algebraic Riccati equations for which the four coe cient matrices form a regular M-matrix K. We prove a property about minimal nonnegative solutions of such an algebraic Riccati equation and its dual equation. And we show that Newton's method, SDA, ADDA are well-de ned and quadratically convergent in non-critical case. Then we prove that ADDA is linearly convergent with rate 1=2 in critical case. As compared to earlier work on solving regular MARE by ADDA, the results we present here are more general. 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And we show that Newton's method, SDA, ADDA are well-de ned and quadratically convergent in non-critical case. Then we prove that ADDA is linearly convergent with rate 1=2 in critical case. As compared to earlier work on solving regular MARE by ADDA, the results we present here are more general. This thesis extends the knowledge of doubling algorithms."],"dc:identifier.doi":["https://doi.org/10.82465/4990"],"dc:identifier.uri":["https://hdl.handle.net/10294/6862"],"dc:language.iso":["en"],"dc:publisher":["Faculty of Graduate Studies and Research, University of Regina"],"dc:title":["Analysis and Numerical Methods for Algebraic Riccati Equations Associated with Regular M-Matrices"],"dc:type":["master thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Master's"],"thesis:degree_name":["Master of Science (MSc)"],"thesis:institution_name":["Faculty of Graduate Studies and Research, University of Regina"]},"updated_at":"2026-07-24T04:03:49Z"}