{"id":"https://openalex.org/W7019256137","doi":null,"title":"Fast and backward stable computation of roots of polynomials, Part IIa: general backward error analysis","display_name":"Fast and backward stable computation of roots of polynomials, Part IIa: general backward error analysis","publication_year":2017,"publication_date":"2017-10-01","ids":{"openalex":"https://openalex.org/W7019256137"},"language":"en","primary_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/596343","doi":null,"is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/596343","pdf_url":"https://lirias.kuleuven.be/retrieve/29d5d2f5-26bc-441d-95ae-db717007c117","source":{"id":"https://openalex.org/S7407055369","display_name":"Lirias","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"TW Reports, Report No. TW683","raw_type":"info:eu-repo/semantics/report"},"parent_works":[],"lineage":["https://openalex.org/W7019256137"],"child_works_count":0,"type":"report","is_traditional":false,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://lirias.kuleuven.be/retrieve/29d5d2f5-26bc-441d-95ae-db717007c117","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091548806","display_name":"Jared L. Aurentz","orcid":"https://orcid.org/0000-0001-7822-6374","observed_orcids":["https://orcid.org/0000-0001-7822-6374"]},"institutions":[{"id":"https://openalex.org/I4210157032","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05e9bn444","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210157032"]},{"id":"https://openalex.org/I63634437","display_name":"Universidad Aut\u00f3noma de Madrid","ror":"https://ror.org/01cby8j38","country_code":"ES","type":"education","lineage":["https://openalex.org/I63634437"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Aurentz, Jared L.","raw_affiliation_strings":["Instituto de Ciencias Matem\u00e1ticas , Universidad Aut\u00f3noma de Madrid , Madrid , Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Ciencias Matem\u00e1ticas , Universidad Aut\u00f3noma de Madrid , Madrid , Spain","institution_ids":["https://openalex.org/I4210157032","https://openalex.org/I63634437"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Mach, Thomas","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Mach, Thomas","raw_affiliation_strings":["Department of Computer Science , KU Leuven","KU Leuven Department of Computer Science Celestijnenlaan 200A - B-3001 Heverlee ( Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science , KU Leuven","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"KU Leuven Department of Computer Science Celestijnenlaan 200A - B-3001 Heverlee ( Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049219826","display_name":"Leonardo Robol","orcid":"https://orcid.org/0000-0002-6545-1748","observed_orcids":["https://orcid.org/0000-0002-6545-1748"]},"institutions":[{"id":"https://openalex.org/I122991210","display_name":"Istituto di Scienza e Tecnologie dell'Informazione \"Alessandro Faedo\"","ror":"https://ror.org/05kacka20","country_code":"IT","type":"facility","lineage":["https://openalex.org/I122991210","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Robol, Leonardo","raw_affiliation_strings":["Istituto di Scienza e Tecnologie dell Informazione 'A. Faedo' (ISTI) , CNR , Pisa , Italy;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Istituto di Scienza e Tecnologie dell Informazione 'A. Faedo' (ISTI) , CNR , Pisa , Italy;","institution_ids":["https://openalex.org/I122991210"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Vandebril, Raf","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Vandebril, Raf","raw_affiliation_strings":["Department of Computer Science , University of Leuven , KU Leuven , Leuven , Belgium;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science , University of Leuven , KU Leuven , Leuven , Belgium;","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006021673","display_name":"David S. Watkins","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I60559429","display_name":"Nazarbayev University","ror":"https://ror.org/052bx8q98","country_code":"KZ","type":"education","lineage":["https://openalex.org/I60559429"]},{"id":"https://openalex.org/I72951846","display_name":"Washington State University","ror":"https://ror.org/05dk0ce17","country_code":"US","type":"education","lineage":["https://openalex.org/I72951846"]}],"countries":["KZ","US"],"is_corresponding":false,"raw_author_name":"Watkins, David S.","raw_affiliation_strings":["Department of Mathematics , School of Science and Technology , Nazarbayev University , 010000 Astana , Kazakhstan;","Department of Mathematics , Washington State University , Pullman , WA 99164-3113 , USA;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , School of Science and Technology , Nazarbayev University , 010000 Astana , Kazakhstan;","institution_ids":["https://openalex.org/I60559429"]},{"raw_affiliation_string":"Department of Mathematics , Washington State University , Pullman , WA 99164-3113 , USA;","institution_ids":["https://openalex.org/I72951846"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.5957000255584717,"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":0.5957000255584717,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.20250000059604645,"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":0.1216999962925911,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polynomial-root-finding","display_name":"polynomial root finding","score":0.8370000123977661},{"id":"https://openalex.org/keywords/backward-error-analysis","display_name":"backward error analysis","score":0.9810000061988831},{"id":"https://openalex.org/keywords/companion-matrix","display_name":"companion matrix","score":0.8830000162124634},{"id":"https://openalex.org/keywords/qz-algorithm","display_name":"QZ algorithm","score":0.8700000047683716},{"id":"https://openalex.org/keywords/generalized-eigenvalue-problem","display_name":"generalized eigenvalue problem","score":0.9779999852180481},{"id":"https://openalex.org/keywords/backward-stability","display_name":"backward stability","score":0.9279999732971191},{"id":"https://openalex.org/keywords/structured-matrices","display_name":"structured matrices","score":0.4129999876022339}],"concepts":[{"id":"https://openalex.org/C144251240","wikidata":"https://www.wikidata.org/wiki/Q7068229","display_name":"Nucleofection","level":4,"score":0.453900009393692},{"id":"https://openalex.org/C2992336715","wikidata":"https://www.wikidata.org/wiki/Q63431143","display_name":"Gestational period","level":4,"score":0.35530000925064087},{"id":"https://openalex.org/C2778283623","wikidata":"https://www.wikidata.org/wiki/Q18032200","display_name":"TSG101","level":5,"score":0.34040001034736633},{"id":"https://openalex.org/C2777158700","wikidata":"https://www.wikidata.org/wiki/Q1419356","display_name":"Hyporeflexia","level":3,"score":0.3176000118255615},{"id":"https://openalex.org/C18743360","wikidata":"https://www.wikidata.org/wiki/Q1208096","display_name":"Diafiltration","level":4,"score":0.31380000710487366},{"id":"https://openalex.org/C2777054765","wikidata":"https://www.wikidata.org/wiki/Q6402731","display_name":"Dysgeusia","level":3,"score":0.3012999892234802},{"id":"https://openalex.org/C2777968768","wikidata":"https://www.wikidata.org/wiki/Q1280161","display_name":"Emperipolesis","level":4,"score":0.28139999508857727},{"id":"https://openalex.org/C145741570","wikidata":"https://www.wikidata.org/wiki/Q7251534","display_name":"Proteogenomics","level":5,"score":0.28130000829696655},{"id":"https://openalex.org/C2781032047","wikidata":"https://www.wikidata.org/wiki/Q938793","display_name":"Articular cartilage damage","level":5,"score":0.28119999170303345},{"id":"https://openalex.org/C135979968","wikidata":"https://www.wikidata.org/wiki/Q609809","display_name":"Protein isoform","level":5,"score":0.28040000796318054},{"id":"https://openalex.org/C104545631","wikidata":"https://www.wikidata.org/wiki/Q464858","display_name":"Demotion","level":3,"score":0.27720001339912415},{"id":"https://openalex.org/C180938184","wikidata":"https://www.wikidata.org/wiki/Q2142270","display_name":"Liquation","level":3,"score":0.2759999930858612},{"id":"https://openalex.org/C2776356786","wikidata":"https://www.wikidata.org/wiki/Q1048573","display_name":"Tubulopathy","level":3,"score":0.2727000117301941},{"id":"https://openalex.org/C133074676","wikidata":"https://www.wikidata.org/wiki/Q428729","display_name":"Fusible alloy","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C2909186138","wikidata":"https://www.wikidata.org/wiki/Q1500373","display_name":"Hyperlactatemia","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C2779627259","wikidata":"https://www.wikidata.org/wiki/Q779763","display_name":"Pretext","level":3,"score":0.2667999863624573},{"id":"https://openalex.org/C2776781215","wikidata":"https://www.wikidata.org/wiki/Q83253","display_name":"Triacetin","level":2,"score":0.2637999951839447},{"id":"https://openalex.org/C2777742743","wikidata":"https://www.wikidata.org/wiki/Q19904005","display_name":"Durvalumab","level":5,"score":0.25690001249313354},{"id":"https://openalex.org/C2777935831","wikidata":"https://www.wikidata.org/wiki/Q3144949","display_name":"Hemopericardium","level":3,"score":0.2535000145435333}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/596343","doi":null,"is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/596343","pdf_url":"https://lirias.kuleuven.be/retrieve/29d5d2f5-26bc-441d-95ae-db717007c117","source":{"id":"https://openalex.org/S7407055369","display_name":"Lirias","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"TW Reports, Report No. TW683","raw_type":"info:eu-repo/semantics/report"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/596343","doi":null,"is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/596343","pdf_url":"https://lirias.kuleuven.be/retrieve/29d5d2f5-26bc-441d-95ae-db717007c117","source":{"id":"https://openalex.org/S7407055369","display_name":"Lirias","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"TW Reports, Report No. TW683","raw_type":"info:eu-repo/semantics/report"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G7099780398","display_name":null,"funder_award_id":"C14/16/056","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"}],"funders":[{"id":"https://openalex.org/F4320322308","display_name":"KU Leuven","ror":"https://ror.org/05f950310"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7019256137.pdf","grobid_xml":"https://content.openalex.org/works/W7019256137.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2511175676"],"related_works":["https://openalex.org/W2885715079","https://openalex.org/W2549154443","https://openalex.org/W1967884132","https://openalex.org/W1918421954","https://openalex.org/W2991958496","https://openalex.org/W2316046929","https://openalex.org/W7098998551","https://openalex.org/W2530356272","https://openalex.org/W3000648079","https://openalex.org/W2130173851"],"abstract_inverted_index":{"This":[0,113],"report":[1,114],"is":[2,37,115],"a":[3,72,81,85,90],"continuation":[4],"of":[5,11,13,42,50,52,80,107],"\"Fast":[6,45],"and":[7,23,31,46,61],"backward":[8,47,56,99,128],"stable":[9,48],"computation":[10,49],"roots":[12,51,79],"polynomials\"":[14],"by":[15,83],"J.":[16],"L.":[17],"Aurentz,":[18],"T.":[19],"Mach,":[20],"R.":[21],"Vandebril,":[22],"D.S.":[24],"Watkins,":[25],"SIAM":[26],"Journal":[27],"on":[28],"Matrix":[29],"Analysis":[30],"Applications,":[32],"36(3):":[33],"942--973,":[34],"2015.":[35],"It":[36],"also":[38],"an":[39,97],"early":[40],"version":[41],"the":[43,78,104,108,119,127],"paper":[44,120],"polynomials,":[53],"Part":[54],"II:":[55],"error":[57,100,129],"analysis;":[58],"companion":[59,62,73,91,109],"matrix":[60,110],"pencil\",":[63],"which":[64],"we":[65,95,122],"have":[66],"submitted":[67],"for":[68,89,126],"publication.":[69],"We":[70],"introduce":[71],"QZ":[74],"algorithm":[75],"that":[76,102,121],"computes":[77],"polynomial":[82],"solving":[84],"generalized":[86],"eigenvalue":[87],"problem":[88],"pencil.":[92,112],"More":[93],"importantly,":[94],"provide":[96],"improved":[98],"analysis":[101,130],"exploits":[103],"special":[105],"structure":[106],"or":[111],"nearly":[116],"identical":[117],"to":[118],"eventually":[123],"submitted,":[124],"except":[125],"in":[131],"Section":[132],"5.":[133]},"counts_by_year":[],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2025-10-10T00:00:00"}