{"id":"https://openalex.org/W2566778665","doi":"https://doi.org/10.1090/mcom/3360","title":"Structured backward error analysis of linearized structured polynomial eigenvalue problems","display_name":"Structured backward error analysis of linearized structured polynomial eigenvalue problems","publication_year":2018,"publication_date":"2018-02-21","ids":{"openalex":"https://openalex.org/W2566778665","doi":"https://doi.org/10.1090/mcom/3360","mag":"2566778665"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3360","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3360","pdf_url":"https://www.ams.org/mcom/2019-88-317/S0025-5718-2018-03360-9/S0025-5718-2018-03360-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2019-88-317/S0025-5718-2018-03360-9/S0025-5718-2018-03360-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076369577","display_name":"Froil\u00e1n M. Dopico","orcid":"https://orcid.org/0000-0001-7779-8960"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Froil\u00e1n Dopico","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911, Legan\u00e9s, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911, Legan\u00e9s, Spain","institution_ids":["https://openalex.org/I50357001"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022647438","display_name":"Javier P\u00e9rez","orcid":"https://orcid.org/0000-0002-5336-3265"},"institutions":[{"id":"https://openalex.org/I6750721","display_name":"University of Montana","ror":"https://ror.org/0078xmk34","country_code":"US","type":"education","lineage":["https://openalex.org/I6750721"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Javier P\u00e9rez","raw_affiliation_strings":["Department of Mathematical Sciences, University of Montana, Montana"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Montana, Montana","institution_ids":["https://openalex.org/I6750721"]}]},{"author_position":"last","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":"Paul Van Dooren","raw_affiliation_strings":["Department of Mathematical Engineering, Universit\u00e9 catholique de Louvain, Avenue Georges Lema\u00eetre 4, B-1348 Louvain-la-Neuve, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Engineering, Universit\u00e9 catholique de Louvain, Avenue Georges Lema\u00eetre 4, B-1348 Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.6488,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.93810833,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"88","issue":"317","first_page":"1189","last_page":"1228"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8249877691268921},{"id":"https://openalex.org/keywords/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.7161959409713745},{"id":"https://openalex.org/keywords/kronecker-delta","display_name":"Kronecker delta","score":0.6091089248657227},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5023303031921387},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.4713568091392517},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.46791747212409973},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.46380022168159485},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45537930727005005},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.45024561882019043},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4496243894100189},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37745821475982666},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12035837769508362}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8249877691268921},{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.7161959409713745},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.6091089248657227},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5023303031921387},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.4713568091392517},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.46791747212409973},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.46380022168159485},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45537930727005005},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.45024561882019043},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4496243894100189},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37745821475982666},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12035837769508362},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/mcom/3360","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3360","pdf_url":"https://www.ams.org/mcom/2019-88-317/S0025-5718-2018-03360-9/S0025-5718-2018-03360-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:dial.uclouvain.be:boreal:200697","is_oa":false,"landing_page_url":"http://hdl.handle.net/2078.1/200697","pdf_url":null,"source":{"id":"https://openalex.org/S4306400166","display_name":"Digital Access to Libraries","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2800384882","host_organization_name":"Harris County Public Library","host_organization_lineage":["https://openalex.org/I2800384882"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, Vol. 88, p. 1189-1228 (2018)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:e-archivo.uc3m.es:10016/32241","is_oa":true,"landing_page_url":"http://hdl.handle.net/10016/32241","pdf_url":null,"source":{"id":"https://openalex.org/S4306400817","display_name":"e-Archivo (Carlos III University of Madrid)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I50357001","host_organization_name":"Universidad Carlos III de Madrid","host_organization_lineage":["https://openalex.org/I50357001"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1090/mcom/3360","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3360","pdf_url":"https://www.ams.org/mcom/2019-88-317/S0025-5718-2018-03360-9/S0025-5718-2018-03360-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G13785451","display_name":null,"funder_award_id":"MTM2015-65798-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G1634352735","display_name":null,"funder_award_id":"MTM-2015-68805_REDT","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G5162831657","display_name":null,"funder_award_id":"MTM-2015-65798-P","funder_id":"https://openalex.org/F4320322681","funder_display_name":"Onderzoeksraad, KU Leuven"},{"id":"https://openalex.org/G647284545","display_name":null,"funder_award_id":"OT/14/074","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G7434063081","display_name":null,"funder_award_id":"OT/14/074","funder_id":"https://openalex.org/F4320322681","funder_display_name":"Onderzoeksraad, KU Leuven"},{"id":"https://openalex.org/G7941806455","display_name":null,"funder_award_id":"MTM-2015-68805-REDT","funder_id":"https://openalex.org/F4320322681","funder_display_name":"Onderzoeksraad, KU Leuven"}],"funders":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320322681","display_name":"Onderzoeksraad, KU Leuven","ror":"https://ror.org/05f950310"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2566778665.pdf"},"referenced_works_count":57,"referenced_works":["https://openalex.org/W142223713","https://openalex.org/W263190779","https://openalex.org/W1481920855","https://openalex.org/W1488435683","https://openalex.org/W1573717114","https://openalex.org/W1576168588","https://openalex.org/W1581306515","https://openalex.org/W1964067206","https://openalex.org/W1965573117","https://openalex.org/W1966369875","https://openalex.org/W1970606629","https://openalex.org/W1974756711","https://openalex.org/W1976384891","https://openalex.org/W1984139226","https://openalex.org/W1994574097","https://openalex.org/W1999834714","https://openalex.org/W2002905417","https://openalex.org/W2008427453","https://openalex.org/W2036174941","https://openalex.org/W2036524199","https://openalex.org/W2042255949","https://openalex.org/W2072004138","https://openalex.org/W2072638881","https://openalex.org/W2073044877","https://openalex.org/W2073389244","https://openalex.org/W2078570317","https://openalex.org/W2083892818","https://openalex.org/W2085537506","https://openalex.org/W2085849252","https://openalex.org/W2086742230","https://openalex.org/W2089101781","https://openalex.org/W2090135779","https://openalex.org/W2092462423","https://openalex.org/W2096718403","https://openalex.org/W2097178696","https://openalex.org/W2097214386","https://openalex.org/W2101137939","https://openalex.org/W2117870622","https://openalex.org/W2123520000","https://openalex.org/W2124986435","https://openalex.org/W2125453344","https://openalex.org/W2128978199","https://openalex.org/W2132177635","https://openalex.org/W2136138364","https://openalex.org/W2140555626","https://openalex.org/W2149913762","https://openalex.org/W2155855077","https://openalex.org/W2174273908","https://openalex.org/W2177331927","https://openalex.org/W2301036970","https://openalex.org/W2395882587","https://openalex.org/W2549165559","https://openalex.org/W2588897321","https://openalex.org/W2602274431","https://openalex.org/W2760096187","https://openalex.org/W2798813531","https://openalex.org/W2962802737"],"related_works":["https://openalex.org/W2177956744","https://openalex.org/W2353337315","https://openalex.org/W4310815509","https://openalex.org/W2739786130","https://openalex.org/W2519757244","https://openalex.org/W233188489","https://openalex.org/W2075390929","https://openalex.org/W1535320509","https://openalex.org/W2769653491","https://openalex.org/W2010853573"],"abstract_inverted_index":{"We":[0],"start":[1],"by":[2,86,158,253],"introducing":[3],"a":[4,24,142,161,170,209,219,270,281,295],"new":[5],"class":[6,13,297],"of":[7,14,30,41,54,66,79,123,149,188,218,298],"structured":[8,31,145,151,186,222],"matrix":[9,20,32,47,103,129,223],"polynomials,":[10,21,130],"namely,":[11,267],"the":[12,39,52,121,131,181,185,189,215,230,242],"M":[15,55,67,97,111,132,162,199],"A":[16,56,68,98,112,133,163,200],"\\mathbf":[17,57,69,99,113,134,164,201],"{M}_A":[18,58,70,100,114,135,165,202],"-structured":[19,59,71,101,115,136,166,203],"to":[22,140,160,196,241],"provide":[23],"common":[25],"framework":[26,137],"for":[27,120,249,274,294],"many":[28],"classes":[29,40,122],"polynomials":[33],"that":[34,95,175,207],"are":[35,76],"important":[36],"in":[37],"applications:":[38],"(skew-)symmetric,":[42,124],"(anti-)":[43],"palindromic,":[44],"and":[45,65,90,93,126,144,233,257,260,289],"alternating":[46,127],"polynomials.":[48],"Then,":[49],"we":[50],"introduce":[51],"families":[53],"strong":[60,300],"block":[61,72,80,116,167,204,250],"minimal":[62,81],"bases":[63,82],"pencils":[64,83,206,226],"Kronecker":[73,117,168,205,251],"pencils,":[74],"which":[75,213],"particular":[77],"examples":[78],"recently":[84],"introduced":[85],"Dopico,":[87,254],"Lawrence,":[88,255],"P\u00e9rez":[89,256],"Van":[91,258],"Dooren,":[92,259],"show":[94],"any":[96],"odd-degree":[102,128],"polynomial":[104,152],"can":[105],"be":[106],"strongly":[107],"linearized":[108],"via":[109],"an":[110],"pencil.":[118],"Finally,":[119],"(anti-)palindromic,":[125],"allows":[138,194],"us":[139,195],"perform":[141],"global":[143],"backward":[146,172,245],"stability":[147],"analysis":[148,193,238,247,272],"complete":[150,178,211],"eigenproblems,":[153],"regular":[154],"or":[155,184],"singular,":[156],"solved":[157],"applying":[159],"pencil":[169],"structurally":[171],"stable":[173],"algorithm":[174,183],"computes":[176],"its":[177,264],"eigenstructure,":[179],"like":[180],"palindromic-QR":[182],"versions":[187],"staircase":[190],"algorithm.":[191],"This":[192],"identify":[197],"those":[198],"yield":[208],"computed":[210],"eigenstructure":[212],"is":[214,269,279,291],"exact":[216],"one":[217],"slightly":[220],"perturbed":[221],"polynomial.":[224],"These":[225],"include":[227],"(modulo":[228],"permutations)":[229],"well-known":[231],"block-tridiagonal":[232],"block-anti-tridiagonal":[234],"structure-preserving":[235,299],"linearizations.":[236,301],"Our":[237],"incorporates":[239],"structure":[240],"recent":[243],"(unstructured)":[244],"error":[246],"performed":[248],"linearizations":[252],"share":[261],"with":[262],"it":[263,268,278,285,290],"key":[265],"features,":[266],"rigorous":[271],"valid":[273,292],"finite":[275],"perturbations,":[276],"i.e.,":[277],"not":[280],"first":[282],"order":[283],"analysis,":[284],"provides":[286],"precise":[287],"bounds,":[288],"simultaneously":[293],"large":[296]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":7}],"updated_date":"2026-08-27T14:10:00.468798","created_date":"2025-10-10T00:00:00"}