{"id":{"repo_id":"regina","oai_identifier":"oai:uregina.scholaris.ca:10294/7713"},"canonical_url":"https://search.dev.ndltd.org/etd/regina/oai:uregina.scholaris.ca:10294/7713","repository":{"repo_id":"regina","name":"University of Regina","base_url":"https://uregina.scholaris.ca/server/oai/request"},"display":{"title":"Studies on quadratic matrix equations and riccati differential equations associated with regular m-matrices","abstract":"The thesis is mainly about the quadratic matrix equation X2- EX- F = 0, where E is a diagonal matrix and F is a regular M-matrix. Quadratic matrix equations of this kind arise in noisy Wiener-Hopf problems for Markov chains. The solution of practical interest is a special M-matrix solution. The existence and uniqueness of M-matrix solutions and some numerical methods for nding the required M-matrix solution are studied by transforming the equation into a nonsymmetric algebraic Riccati equation for which the four coe cient matrices form a regular M-matrix. We also discuss the initial value problem for a matrix Riccati di erential equation associated with a regular M-matrix. We show that for suitable initial matrices X0, the initial value problem has a global solution X(t) on [0;1): Moreover, we show that X(t) converges, as t ! 1, to the stable equilibrium solution, which is the minimal nonnegative solution of corresponding algebraic Riccati equation.","abstract_html":"The thesis is mainly about the quadratic matrix equation X2- EX- F = 0, where E is a diagonal matrix and F is a regular M-matrix. Quadratic matrix equations of this kind arise in noisy Wiener-Hopf problems for Markov chains. The solution of practical interest is a special M-matrix solution. The existence and uniqueness of M-matrix solutions and some numerical methods for nding the required M-matrix solution are studied by transforming the equation into a nonsymmetric algebraic Riccati equation for which the four coe cient matrices form a regular M-matrix. We also discuss the initial value problem for a matrix Riccati di erential equation associated with a regular M-matrix. We show that for suitable initial matrices X0, the initial value problem has a global solution X(t) on [0;1): Moreover, we show that X(t) converges, as t ! 1, to the stable equilibrium solution, which is the minimal nonnegative solution of corresponding algebraic Riccati equation.","abstract_has_math":false,"creators":["Roy, Anupam"],"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":["Floricel, Remus"],"year":2017,"date_issued":"2017-01","date_published":"2017-01","updated_at":"2026-07-24T04:03:34Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.82465/4178"],"render_values":[{"text":"https://doi.org/10.82465/4178","href":"https://doi.org/10.82465/4178","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10294/7713","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":["Floricel, Remus"]},{"key":"dc:creator","label":"Author","values":["Roy, Anupam"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-06-19T22:48:15Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-06-19T22:48:15Z"]},{"key":"dc:date.issued","label":"Date","values":["2017-01"]},{"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/10.82465/4178"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10294/7713"]}]},{"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, 57 p."]},{"key":"dc:description.abstract","label":"Abstract","values":["The thesis is mainly about the quadratic matrix equation X2- EX- F = 0, where E is a diagonal matrix and F is a regular M-matrix. Quadratic matrix equations of this kind arise in noisy Wiener-Hopf problems for Markov chains. The solution of practical interest is a special M-matrix solution. The existence and uniqueness of M-matrix solutions and some numerical methods for nding the required M-matrix solution are studied by transforming the equation into a nonsymmetric algebraic Riccati equation for which the four coe cient matrices form a regular M-matrix. We also discuss the initial value problem for a matrix Riccati di erential equation associated with a regular M-matrix. We show that for suitable initial matrices X0, the initial value problem has a global solution X(t) on [0;1): Moreover, we show that X(t) converges, as t ! 1, to the stable equilibrium solution, which is the minimal nonnegative solution of corresponding algebraic Riccati equation."]},{"key":"dc:title","label":"Title","values":["Studies on quadratic matrix equations and riccati differential equations associated with regular m-matrices"]}]}],"canonical_facts":{"dc:contributor.advisor":["Guo, Chun-Hua"],"dc:contributor.committeemember":["Floricel, Remus"],"dc:creator":["Roy, Anupam"],"dc:date.accessioned":["2017-06-19T22:48:15Z"],"dc:date.available":["2017-06-19T22:48:15Z"],"dc:date.issued":["2017-01"],"dc:description":["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, 57 p."],"dc:description.abstract":["The thesis is mainly about the quadratic matrix equation X2- EX- F = 0, where E is a diagonal matrix and F is a regular M-matrix. Quadratic matrix equations of this kind arise in noisy Wiener-Hopf problems for Markov chains. The solution of practical interest is a special M-matrix solution. The existence and uniqueness of M-matrix solutions and some numerical methods for nding the required M-matrix solution are studied by transforming the equation into a nonsymmetric algebraic Riccati equation for which the four coe cient matrices form a regular M-matrix. We also discuss the initial value problem for a matrix Riccati di erential equation associated with a regular M-matrix. We show that for suitable initial matrices X0, the initial value problem has a global solution X(t) on [0;1): Moreover, we show that X(t) converges, as t ! 1, to the stable equilibrium solution, which is the minimal nonnegative solution of corresponding algebraic Riccati equation."],"dc:identifier.doi":["https://doi.org/10.82465/4178"],"dc:identifier.uri":["https://hdl.handle.net/10294/7713"],"dc:language.iso":["en"],"dc:publisher":["Faculty of Graduate Studies and Research, University of Regina"],"dc:title":["Studies on quadratic matrix equations and riccati differential 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":"2026-07-24T04:03:34Z"}