{"id":"https://openalex.org/W2115917296","doi":"https://doi.org/10.1109/cdc.2003.1272970","title":"A newton algorithm for invariant subspace computation with large basins of attraction","display_name":"A newton algorithm for invariant subspace computation with large basins of attraction","publication_year":2004,"publication_date":"2004-07-08","ids":{"openalex":"https://openalex.org/W2115917296","doi":"https://doi.org/10.1109/cdc.2003.1272970","mag":"2115917296"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2003.1272970","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2003.1272970","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034347171","display_name":"P.-A. Absil","orcid":"https://orcid.org/0000-0003-2946-4178"},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]},{"id":"https://openalex.org/I17653759","display_name":"Fund for Scientific Research","ror":"https://ror.org/03q83t159","country_code":"BE","type":"nonprofit","lineage":["https://openalex.org/I17653759"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"P.-A. Absil","raw_affiliation_strings":["Aspirant du F. N. R. S. (Belgian National Fund for Scientific Research), Belgium","Department of Electrical-Engineering and Computer Science,Institut hlontefiore (B28), Universit\u00e9 de Li\u00e8ge Sart-Tilman, Liege, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Aspirant du F. N. R. S. (Belgian National Fund for Scientific Research), Belgium","institution_ids":["https://openalex.org/I17653759"]},{"raw_affiliation_string":"Department of Electrical-Engineering and Computer Science,Institut hlontefiore (B28), Universit\u00e9 de Li\u00e8ge Sart-Tilman, Liege, Belgium","institution_ids":["https://openalex.org/I157674565"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067642477","display_name":"Rodolphe Sepulchre","orcid":"https://orcid.org/0000-0002-7047-3124"},"institutions":[{"id":"https://openalex.org/I157674565","display_name":"University of Li\u00e8ge","ror":"https://ror.org/00afp2z80","country_code":"BE","type":"education","lineage":["https://openalex.org/I157674565"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"R. Sepulchre","raw_affiliation_strings":["Department of Electrical-Engineering and Computer Science,Institut hlontefiore (B28), Universit\u00e9 de Li\u00e8ge Sart-Tilman, Liege, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical-Engineering and Computer Science,Institut hlontefiore (B28), Universit\u00e9 de Li\u00e8ge Sart-Tilman, Liege, Belgium","institution_ids":["https://openalex.org/I157674565"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036923077","display_name":"Paul Van Dooren","orcid":"https://orcid.org/0000-0002-0115-9932"},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"P. Van Dooren","raw_affiliation_strings":["Department of Mathematical Engineering, Universit\u00e9 Catholique de Louvain, Louvain-la-Neuve, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Engineering, Universit\u00e9 Catholique de Louvain, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011097720","display_name":"Robert Mahony","orcid":"https://orcid.org/0000-0002-7803-2868"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"R. Mahony","raw_affiliation_strings":["Demrtment of Enaineering, Australian National University, ACT, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Demrtment of Enaineering, Australian National University, ACT, Australia","institution_ids":["https://openalex.org/I118347636"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"3","issue":null,"first_page":"2352","last_page":"2357"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.7484629154205322},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.7106963396072388},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6470678448677063},{"id":"https://openalex.org/keywords/invariant-subspace","display_name":"Invariant subspace","score":0.6369284391403198},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5913400053977966},{"id":"https://openalex.org/keywords/attraction","display_name":"Attraction","score":0.5577269792556763},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5425243377685547},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5320257544517517},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.4467353820800781},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.423663854598999},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4153934717178345},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3523291051387787},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33252668380737305},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3292607069015503},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2124263346195221},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1886599063873291},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.10777917504310608},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07236313819885254}],"concepts":[{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.7484629154205322},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.7106963396072388},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6470678448677063},{"id":"https://openalex.org/C2777059694","wikidata":"https://www.wikidata.org/wiki/Q2706744","display_name":"Invariant subspace","level":3,"score":0.6369284391403198},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5913400053977966},{"id":"https://openalex.org/C2778364177","wikidata":"https://www.wikidata.org/wiki/Q2247133","display_name":"Attraction","level":2,"score":0.5577269792556763},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5425243377685547},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5320257544517517},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.4467353820800781},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.423663854598999},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4153934717178345},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3523291051387787},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33252668380737305},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3292607069015503},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2124263346195221},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1886599063873291},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10777917504310608},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07236313819885254},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/cdc.2003.1272970","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2003.1272970","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)","raw_type":"proceedings-article"},{"id":"pmh:oai:dial.uclouvain.be:boreal:80613","is_oa":false,"landing_page_url":"http://hdl.handle.net/2078.1/80613","pdf_url":null,"source":{"id":"https://openalex.org/S4306401902","display_name":"Digital Access to Libraries (Universit\u00e9 catholique de Louvain (UCL), l'Universit\u00e9 de Namur (UNamur) and the Universit\u00e9 Saint-Louis (USL-B))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I95674353","host_organization_name":"UCLouvain","host_organization_lineage":["https://openalex.org/I95674353"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:generic.eprints.org:577539","is_oa":false,"landing_page_url":"http://publications.eng.cam.ac.uk/577539/","pdf_url":null,"source":{"id":"https://openalex.org/S4406922847","display_name":"Cambridge University Engineering Department Publications Database","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/733798578","is_oa":false,"landing_page_url":"https://hdl.handle.net/1885/733798578","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the IEEE Conference on Decision and Control","raw_type":"Conference paper"},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/74499","is_oa":false,"landing_page_url":"http://hdl.handle.net/1885/74499","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings of the 42nd IEEE Conference on Decision and Control","raw_type":"Conference paper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1492579554","https://openalex.org/W1877848529","https://openalex.org/W1982472447","https://openalex.org/W1983592997","https://openalex.org/W2005400753","https://openalex.org/W2028324955","https://openalex.org/W2045512849","https://openalex.org/W2049460408","https://openalex.org/W2051410107","https://openalex.org/W2059586807","https://openalex.org/W2064559422","https://openalex.org/W2068484625","https://openalex.org/W2084839116","https://openalex.org/W2085594561","https://openalex.org/W2090859773","https://openalex.org/W2136289064","https://openalex.org/W2147631863","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W3100286349","https://openalex.org/W2896134808","https://openalex.org/W3172436493","https://openalex.org/W4287164812","https://openalex.org/W2957492749","https://openalex.org/W1887135636","https://openalex.org/W2386063599","https://openalex.org/W1975884855","https://openalex.org/W3213150849","https://openalex.org/W4285605394"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,10,21,26,41,54,61,66,71],"global":[3],"behaviour":[4],"of":[5,23,25,33,40,63,65],"a":[6],"Newton":[7],"algorithm":[8,42],"on":[9],"Grassmann":[11],"manifold":[12],"for":[13,52],"invariant":[14,27,67],"subspace":[15],"computation.":[16],"It":[17],"is":[18,47,56],"shown":[19,57],"that":[20],"basins":[22,62],"attraction":[24,64],"subspaces":[28,68],"may":[29],"collapse":[30],"in":[31],"case":[32],"small":[34],"eigenvalue":[35],"gaps.":[36],"A":[37,49],"Levenberg-Marquardt-like":[38],"modification":[39],"with":[43],"low":[44],"numerical":[45],"cost":[46],"proposed.":[48],"simple":[50],"strategy":[51],"choosing":[53],"parameter":[55],"to":[58],"dramatically":[59],"enlarge":[60],"while":[69],"preserving":[70],"fast":[72],"local":[73],"convergence.":[74]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
