{"id":"https://openalex.org/W2014075804","doi":"https://doi.org/10.1137/s0895479891218922","title":"The Schur Algorithm for Matrix-Valued Meromorphic Functions","display_name":"The Schur Algorithm for Matrix-Valued Meromorphic Functions","publication_year":1994,"publication_date":"1994-01-01","ids":{"openalex":"https://openalex.org/W2014075804","doi":"https://doi.org/10.1137/s0895479891218922","mag":"2014075804"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479891218922","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479891218922","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085683792","display_name":"Reuven Ackner","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Reuven Ackner","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040128027","display_name":"H. Lev-Ari","orcid":"https://orcid.org/0000-0003-1937-5702"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hanoch Lev-Ari","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5014088470","display_name":"T. Kailath","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas Kailath","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8395,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.85463842,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"15","issue":"1","first_page":"140","last_page":"150"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9994000196456909,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9980999827384949,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8311210870742798},{"id":"https://openalex.org/keywords/meromorphic-function","display_name":"Meromorphic function","score":0.7382560968399048},{"id":"https://openalex.org/keywords/unit-circle","display_name":"Unit circle","score":0.7370178699493408},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5789132118225098},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5092812776565552},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49225202202796936},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.46694862842559814},{"id":"https://openalex.org/keywords/schur-decomposition","display_name":"Schur decomposition","score":0.43439921736717224},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4331137537956238},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4306495487689972},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3403695821762085},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.26225170493125916},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13496538996696472}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8311210870742798},{"id":"https://openalex.org/C190333341","wikidata":"https://www.wikidata.org/wiki/Q217616","display_name":"Meromorphic function","level":2,"score":0.7382560968399048},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.7370178699493408},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5789132118225098},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5092812776565552},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49225202202796936},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.46694862842559814},{"id":"https://openalex.org/C99383703","wikidata":"https://www.wikidata.org/wiki/Q1064218","display_name":"Schur decomposition","level":4,"score":0.43439921736717224},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4331137537956238},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4306495487689972},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3403695821762085},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.26225170493125916},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13496538996696472},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479891218922","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479891218922","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1504633463","https://openalex.org/W1519226469","https://openalex.org/W1968249360","https://openalex.org/W1986979384","https://openalex.org/W2005049658","https://openalex.org/W2007338024","https://openalex.org/W2031477115","https://openalex.org/W2068164442","https://openalex.org/W2082777584","https://openalex.org/W2083862580","https://openalex.org/W2084810505","https://openalex.org/W2120037458","https://openalex.org/W2123539155","https://openalex.org/W2130274775","https://openalex.org/W2145142884","https://openalex.org/W2331560164","https://openalex.org/W4247846618"],"related_works":["https://openalex.org/W2100927581","https://openalex.org/W4245038494","https://openalex.org/W2365415664","https://openalex.org/W2144415757","https://openalex.org/W137814303","https://openalex.org/W3094161286","https://openalex.org/W2051346221","https://openalex.org/W2055400126","https://openalex.org/W2101668498","https://openalex.org/W2556446323"],"abstract_inverted_index":{"This":[0,78],"article":[1,34,79],"extends":[2],"the":[3,14,26,41,54,64,70,75,88,96,99,104,111,128],"classical":[4],"Schur":[5],"algorithm":[6,89,129],"to":[7,82,110],"matrix-valued":[8],"functions":[9],"that":[10,130],"are":[11],"bounded":[12],"on":[13],"unit":[15,27,76,105],"circle":[16],"and":[17,90],"have":[18],"a":[19,57,92,114,121],"finite":[20],"number":[21,65,71,100],"of":[22,44,59,66,72,101,107,113],"Smith\u2013McMillan":[23],"poles":[24,73,102],"inside":[25,103],"disc.":[28,77],"With":[29],"each":[30,108],"such":[31],"function":[32],"this":[33],"associates":[35],"two":[36],"infinite":[37],"sequences:":[38],"one":[39,50],"is":[40,56,120],"well-known":[42],"sequence":[43,58],"reflection":[45],"coefficients":[46],"(all":[47],"less":[48],"than":[49],"in":[51],"magnitude),":[52],"whereas":[53],"other":[55],"signs.":[60],"Under":[61],"certain":[62,115],"assumptions,":[63],"negative":[67],"signs":[68],"equals":[69],"within":[74],"shows":[80],"how":[81],"solve":[83],"tangential":[84],"interpolation":[85],"problems":[86],"using":[87],"gives":[91],"simple":[93],"proof":[94],"for":[95,125],"connection":[97],"between":[98],"disc":[106],"solution":[109],"inertia":[112],"Pick":[116],"matrix.":[117],"Also":[118],"described":[119],"numerically":[122],"efficient":[123],"procedure":[124],"carrying":[126],"out":[127],"involves":[131],"only":[132],"scalar":[133],"operations.":[134]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}