{"id":"https://openalex.org/W2077034598","doi":"https://doi.org/10.1137/130904508","title":"Fast Reduction of Generalized Companion Matrix Pairs for Barycentric Lagrange Interpolants","display_name":"Fast Reduction of Generalized Companion Matrix Pairs for Barycentric Lagrange Interpolants","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2077034598","doi":"https://doi.org/10.1137/130904508","mag":"2077034598"},"language":"en","primary_location":{"id":"doi:10.1137/130904508","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130904508","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/A5017519638","display_name":"Piers W. Lawrence","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Piers W. Lawrence","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5017519638"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1871,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.87941224,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"34","issue":"3","first_page":"1277","last_page":"1300"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9976999759674072,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.9070092439651489},{"id":"https://openalex.org/keywords/barycentric-coordinate-system","display_name":"Barycentric coordinate system","score":0.8134309649467468},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7812825441360474},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7433330416679382},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6176484227180481},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5697759389877319},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5308215022087097},{"id":"https://openalex.org/keywords/vandermonde-matrix","display_name":"Vandermonde matrix","score":0.45211565494537354},{"id":"https://openalex.org/keywords/lagrange-polynomial","display_name":"Lagrange polynomial","score":0.42521989345550537},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3684123754501343},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1987251341342926},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.17570513486862183},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1132727861404419},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0676785409450531}],"concepts":[{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.9070092439651489},{"id":"https://openalex.org/C128356825","wikidata":"https://www.wikidata.org/wiki/Q738422","display_name":"Barycentric coordinate system","level":2,"score":0.8134309649467468},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7812825441360474},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7433330416679382},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6176484227180481},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5697759389877319},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5308215022087097},{"id":"https://openalex.org/C55294529","wikidata":"https://www.wikidata.org/wiki/Q579544","display_name":"Vandermonde matrix","level":3,"score":0.45211565494537354},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.42521989345550537},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3684123754501343},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1987251341342926},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.17570513486862183},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1132727861404419},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0676785409450531},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130904508","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130904508","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W406819860","https://openalex.org/W1971545142","https://openalex.org/W1976998625","https://openalex.org/W1981115560","https://openalex.org/W1986899147","https://openalex.org/W2019645585","https://openalex.org/W2029969454","https://openalex.org/W2029981163","https://openalex.org/W2044080186","https://openalex.org/W2049897010","https://openalex.org/W2056522847","https://openalex.org/W2068351005","https://openalex.org/W2069188165","https://openalex.org/W2070461982","https://openalex.org/W2117948699","https://openalex.org/W2130694104","https://openalex.org/W2133549820","https://openalex.org/W2140412681","https://openalex.org/W2149281222"],"related_works":["https://openalex.org/W1648644969","https://openalex.org/W2358123980","https://openalex.org/W3003354345","https://openalex.org/W2364141700","https://openalex.org/W4313216527","https://openalex.org/W4391388031","https://openalex.org/W3092940009","https://openalex.org/W2920972371","https://openalex.org/W1986899147","https://openalex.org/W2898718453"],"abstract_inverted_index":{"For":[0,21],"a":[1,15,33,100],"barycentric":[2,145],"Lagrange":[3,146],"interpolant":[4,75],"$p(z)$,":[5],"the":[6,12,25,53,70,74,91,106,110,118,124,138,142],"roots":[7,143],"of":[8,14,73,94,105,123,140,144],"$p(z)$":[9,95],"are":[10,76,96],"exactly":[11],"eigenvalues":[13,108],"generalized":[16],"companion":[17],"matrix":[18,26,60,112],"pair":[19,27,34,54,61,113],"$(\\mathbf{A},\\mathbf{B})$.":[20],"real":[22],"interpolation":[23],"nodes,":[24],"$(\\mathbf{A},\\mathbf{B})$":[28,55,62],"can":[29],"be":[30,81,149],"reduced":[31,111],"to":[32,56,102],"$(\\mathbf{H},\\mathbf{B})$,":[35,114],"where":[36],"$\\mathbf{H}$":[37],"has":[38,63],"tridiagonal":[39,119],"plus":[40,120],"rank-one":[41,121],"structure.":[42],"In":[43],"this":[44],"paper":[45],"we":[46],"propose":[47,86],"two":[48,64],"fast":[49,130],"algorithms":[50,132],"for":[51,88,134],"reducing":[52],"Hessenberg-triangular":[57],"form.":[58],"The":[59],"spurious":[65],"infinite":[66,83,107],"eigenvalues,":[67],"and":[68,98],"if":[69],"leading":[71,92],"coefficients":[72,93],"zero,":[77,97],"there":[78],"will":[79],"also":[80],"other":[82],"eigenvalues.":[84],"We":[85],"tools":[87],"detecting":[89],"when":[90],"describe":[99],"procedure":[101],"deflate":[103],"all":[104],"from":[109],"while":[115],"still":[116],"maintaining":[117],"structure":[122],"resulting":[125],"standard":[126],"eigenvalue":[127],"problem.":[128],"Since":[129],"$QR$":[131],"exist":[133],"such":[135],"structured":[136],"matrices,":[137],"complexity":[139],"computing":[141],"interpolants":[147],"could":[148],"significantly":[150],"reduced.":[151]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
