{"id":"https://openalex.org/W2613089370","doi":"https://doi.org/10.1137/17m1125182","title":"Reduction of Matrix Polynomials to Simpler Forms","display_name":"Reduction of Matrix Polynomials to Simpler Forms","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2613089370","doi":"https://doi.org/10.1137/17m1125182","mag":"2613089370"},"language":"en","primary_location":{"id":"doi:10.1137/17m1125182","is_oa":true,"landing_page_url":"https://doi.org/10.1137/17m1125182","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/17M1125182","source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/17M1125182","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008129578","display_name":"Yuji Nakatsukasa","orcid":"https://orcid.org/0000-0001-7911-1501"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuji Nakatsukasa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038987851","display_name":"Leo Taslaman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leo Taslaman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059791596","display_name":"Fran\u00e7oise Tisseur","orcid":"https://orcid.org/0000-0002-1011-2570"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fran\u00e7oise Tisseur","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059067253","display_name":"I. Zaballa","orcid":"https://orcid.org/0000-0002-6113-9079"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ion Zaballa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":{"value":2571,"currency":"EUR","value_usd":2772},"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.02059728,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"39","issue":"1","first_page":"148","last_page":"177"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9929999709129333,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9824000000953674,"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/unimodular-matrix","display_name":"Unimodular matrix","score":0.8035054206848145},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.776397705078125},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.763059139251709},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.6226383447647095},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.6190490126609802},{"id":"https://openalex.org/keywords/matrix-similarity","display_name":"Matrix similarity","score":0.6173157095909119},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.5728604793548584},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5447205305099487},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.4745241701602936},{"id":"https://openalex.org/keywords/schur-decomposition","display_name":"Schur decomposition","score":0.470774382352829},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.41981634497642517},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.41370105743408203},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39204108715057373},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.34804224967956543},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3301233649253845},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.29651400446891785},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1757471263408661},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10842317342758179}],"concepts":[{"id":"https://openalex.org/C201958917","wikidata":"https://www.wikidata.org/wiki/Q1367055","display_name":"Unimodular matrix","level":2,"score":0.8035054206848145},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.776397705078125},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.763059139251709},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6226383447647095},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.6190490126609802},{"id":"https://openalex.org/C39739852","wikidata":"https://www.wikidata.org/wiki/Q254491","display_name":"Matrix similarity","level":3,"score":0.6173157095909119},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.5728604793548584},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5447205305099487},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.4745241701602936},{"id":"https://openalex.org/C99383703","wikidata":"https://www.wikidata.org/wiki/Q1064218","display_name":"Schur decomposition","level":4,"score":0.470774382352829},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.41981634497642517},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.41370105743408203},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39204108715057373},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.34804224967956543},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3301233649253845},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.29651400446891785},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1757471263408661},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10842317342758179},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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:10.1137/17m1125182","is_oa":true,"landing_page_url":"https://doi.org/10.1137/17m1125182","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/17M1125182","source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/55534813-cc59-46c9-8b68-b8e6b92a4a54","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/55534813-cc59-46c9-8b68-b8e6b92a4a54","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nakatsukasa, Y, Taslaman, L, Tisseur, F & Zaballa, I 2018, 'REDUCTION OF MATRIX POLYNOMIALS TO SIMPLER FORMS', SIAM Journal on Matrix Analysis and Applications, vol. 39, no. 1, pp. 148. https://doi.org/10.1137/17M1125182","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2539","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400452","display_name":"MIMS EPrints (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"MIMS Preprint"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:c22b5749-45a5-411e-bcf1-0e5e64ceff0c","is_oa":true,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:c22b5749-45a5-411e-bcf1-0e5e64ceff0c","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal article"},{"id":"pmh:oai:pure.atira.dk:publications/55534813-cc59-46c9-8b68-b8e6b92a4a54","is_oa":true,"landing_page_url":"https://www.research.manchester.ac.uk/portal/en/publications/reduction-of-matrix-polynomials-to-simpler-forms(55534813-cc59-46c9-8b68-b8e6b92a4a54).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Nakatsukasa, Y, Taslaman, L, Tisseur, F & Zaballa, I 2018, 'REDUCTION OF MATRIX POLYNOMIALS TO SIMPLER FORMS', SIAM Journal on Matrix Analysis and Applications, vol. 39, no. 1, pp. 148. https://doi.org/10.1137/17M1125182","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1137/17m1125182","is_oa":true,"landing_page_url":"https://doi.org/10.1137/17m1125182","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/17M1125182","source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2449384599","display_name":null,"funder_award_id":"EP/I005293/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6757365500","display_name":null,"funder_award_id":"EP/I005293","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W36999706","https://openalex.org/W1568240140","https://openalex.org/W1987904664","https://openalex.org/W2000537011","https://openalex.org/W2003630367","https://openalex.org/W2015344163","https://openalex.org/W2016086537","https://openalex.org/W2020093844","https://openalex.org/W2063156073","https://openalex.org/W2070680717","https://openalex.org/W2088876089","https://openalex.org/W2121461537","https://openalex.org/W2124953282","https://openalex.org/W2153333084","https://openalex.org/W2160535817","https://openalex.org/W2404150775","https://openalex.org/W2610857016","https://openalex.org/W2798909945","https://openalex.org/W4252157471"],"related_works":["https://openalex.org/W1975201729","https://openalex.org/W2074771309","https://openalex.org/W2064598248","https://openalex.org/W3092306907","https://openalex.org/W2551678916","https://openalex.org/W1985400098","https://openalex.org/W3115487577","https://openalex.org/W1510582995","https://openalex.org/W1986380039","https://openalex.org/W2613089370"],"abstract_inverted_index":{"A":[0],"square":[1],"matrix":[2,30,46,62,96,135,145],"can":[3,66],"be":[4,67],"reduced":[5,72,156],"to":[6,17,69,82,93,102,118,122,130,143,153,158],"simpler":[7,104],"form":[8,108],"via":[9],"similarity":[10,40,127],"transformations.":[11,41],"Here":[12],"\u201csimpler":[13],"form\u201d":[14],"may":[15],"refer":[16],"diagonal":[18],"(when":[19],"possible),":[20],"triangular":[21],"(Schur),":[22],"or":[23],"Hessenberg":[24],"form.":[25],"Similar":[26],"reductions":[27],"exist":[28],"for":[29,52],"pencils":[31],"if":[32],"we":[33,75,88,150],"consider":[34],"general":[35],"equivalence":[36],"transformations":[37,65,128,140],"instead":[38,137],"of":[39,133,138],"For":[42,61],"both":[43],"matrices":[44],"and":[45,113],"pencils,":[47],"well-established":[48],"algorithms":[49],"are":[50,56],"available":[51],"each":[53],"reduction,":[54],"which":[55],"useful":[57],"in":[58],"various":[59],"applications.":[60],"polynomials,":[63],"unimodular":[64,139],"used":[68],"achieve":[70],"the":[71,111,114,134,144],"forms":[73,157],"but":[74],"do":[76],"not":[77],"have":[78],"a":[79,90,95,103,131],"practical":[80,91],"way":[81],"compute":[83],"them.":[84],"In":[85],"this":[86],"work":[87,123],"introduce":[89],"means":[92],"reduce":[94],"polynomial":[97,136],"with":[98,124],"nonsingular":[99],"leading":[100],"coefficient":[101],"(diagonal,":[105],"triangular,":[106],"Hessenberg)":[107],"while":[109],"preserving":[110,126],"degree":[112],"eigenstructure.":[115],"The":[116],"key":[117],"our":[119],"approach":[120],"is":[121],"structure":[125],"applied":[129,141],"linearization":[132],"directly":[142],"polynomial.":[146],"As":[147],"an":[148],"application,":[149],"illustrate":[151],"how":[152],"use":[154],"these":[155],"solve":[159],"parameterized":[160],"linear":[161],"systems.":[162]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}