{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/37745"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/37745","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Interpolation by rational matrix functions with minimal McMillan degree","abstract":"Interpolation conditions on rational matrix functions expressed in terms of residues are studied. As a compact way of expressing tangential interpolation conditions of arbitrarily high multiplicity possibly from both sides simultaneously, interpolation conditions are represented in terms of residues. The minimal possible complexity, measured by the McMillan degree, of interpolants is found in terms of the controllability and the observability indices of certain pairs of matrices which are part of given data. An interpolant of such complexity is obtained in realization form. This leads to another approach to the partial realization problem. As a generalization of the well-known Lagrange interpolation problem for scalar polynomials, the problem of seeking for a matrix polynomial interpolant of low complexity is studied. The main tool is state space methods borrowed from systems theory. After adoption of state space methods, problems concerning rational matrix functions are reduced to the realm of linear algebra.","abstract_html":"Interpolation conditions on rational matrix functions expressed in terms of residues are studied. As a compact way of expressing tangential interpolation conditions of arbitrarily high multiplicity possibly from both sides simultaneously, interpolation conditions are represented in terms of residues. The minimal possible complexity, measured by the McMillan degree, of interpolants is found in terms of the controllability and the observability indices of certain pairs of matrices which are part of given data. An interpolant of such complexity is obtained in realization form. This leads to another approach to the partial realization problem. As a generalization of the well-known Lagrange interpolation problem for scalar polynomials, the problem of seeking for a matrix polynomial interpolant of low complexity is studied. The main tool is state space methods borrowed from systems theory. After adoption of state space methods, problems concerning rational matrix functions are reduced to the realm of linear algebra.","abstract_has_math":false,"creators":["Kang, Jeongook Kim"],"institution":"Virginia Tech","degree_name":"Ph. D.","degree_level":"doctoral","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Ball, Joseph A."],"committee_members":["Hannsgen, Kenneth B.","Herdman, Terry L.","Kohler, Werner E.","Thomson, James E."],"year":1990,"date_issued":"1990-12-05","date_published":"1990-12-05","updated_at":"2026-07-22T22:20:03Z","subjects":[],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-05112006-154752"],"render_values":[{"text":"etd-05112006-154752","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/37745","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Ball, Joseph A."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Hannsgen, Kenneth B.","Herdman, Terry L.","Kohler, Werner E.","Thomson, James E."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Kang, Jeongook Kim"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:10:52Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:10:52Z","2006-05-11"]},{"key":"dc:date.issued","label":"Date","values":["1990-12-05"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-05112006-154752"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/37745"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Interpolation conditions on rational matrix functions expressed in terms of residues are studied. As a compact way of expressing tangential interpolation conditions of arbitrarily high multiplicity possibly from both sides simultaneously, interpolation conditions are represented in terms of residues. The minimal possible complexity, measured by the McMillan degree, of interpolants is found in terms of the controllability and the observability indices of certain pairs of matrices which are part of given data. An interpolant of such complexity is obtained in realization form. This leads to another approach to the partial realization problem. As a generalization of the well-known Lagrange interpolation problem for scalar polynomials, the problem of seeking for a matrix polynomial interpolant of low complexity is studied. The main tool is state space methods borrowed from systems theory. After adoption of state space methods, problems concerning rational matrix functions are reduced to the realm of linear algebra."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["BTD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Interpolation by rational matrix functions with minimal McMillan degree"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Ball, Joseph A."],"dc:contributor.committeemember":["Hannsgen, Kenneth B.","Herdman, Terry L.","Kohler, Werner E.","Thomson, James E."],"dc:contributor.department":["Mathematics"],"dc:creator":["Kang, Jeongook Kim"],"dc:date.accessioned":["2014-03-14T21:10:52Z"],"dc:date.available":["2014-03-14T21:10:52Z","2006-05-11"],"dc:date.issued":["1990-12-05"],"dc:description.abstract":["Interpolation conditions on rational matrix functions expressed in terms of residues are studied. As a compact way of expressing tangential interpolation conditions of arbitrarily high multiplicity possibly from both sides simultaneously, interpolation conditions are represented in terms of residues. The minimal possible complexity, measured by the McMillan degree, of interpolants is found in terms of the controllability and the observability indices of certain pairs of matrices which are part of given data. An interpolant of such complexity is obtained in realization form. This leads to another approach to the partial realization problem. As a generalization of the well-known Lagrange interpolation problem for scalar polynomials, the problem of seeking for a matrix polynomial interpolant of low complexity is studied. The main tool is state space methods borrowed from systems theory. After adoption of state space methods, problems concerning rational matrix functions are reduced to the realm of linear algebra."],"dc:description.degree":["Ph. D."],"dc:format.medium":["BTD"],"dc:format.mimetype":["application/pdf"],"dc:identifier.other":["etd-05112006-154752"],"dc:identifier.uri":["http://hdl.handle.net/10919/37745"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["Interpolation by rational matrix functions with minimal McMillan degree"],"dc:type":["Dissertation"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph. D."],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:03Z"}