{"id":"https://openalex.org/W2008280494","doi":"https://doi.org/10.1145/2331684.2331706","title":"Numerical stability of barycentric Hermite root-finding","display_name":"Numerical stability of barycentric Hermite root-finding","publication_year":2012,"publication_date":"2012-06-07","ids":{"openalex":"https://openalex.org/W2008280494","doi":"https://doi.org/10.1145/2331684.2331706","mag":"2008280494"},"language":"en","primary_location":{"id":"doi:10.1145/2331684.2331706","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2331684.2331706","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation","raw_type":"proceedings-article"},"type":"conference-paper","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":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Piers W. Lawrence","raw_affiliation_strings":["ORCCA, UWO, London, ON, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ORCCA, UWO, London, ON, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044605948","display_name":"Robert M. Corless","orcid":"https://orcid.org/0000-0003-0515-1572"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Robert M. Corless","raw_affiliation_strings":["ORCCA, UWO, London, ON, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ORCCA, UWO, London, ON, Canada","institution_ids":["https://openalex.org/I125749732"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I125749732"],"apc_list":null,"apc_paid":null,"fwci":1.7149,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.8233835,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"147","last_page":"148"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987999796867371,"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":0.9987999796867371,"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":0.9890000224113464,"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/T13126","display_name":"Scientific Research and Discoveries","score":0.9789999723434448,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.8012923002243042},{"id":"https://openalex.org/keywords/properties-of-polynomial-roots","display_name":"Properties of polynomial roots","score":0.7363941073417664},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7085713148117065},{"id":"https://openalex.org/keywords/characteristic-polynomial","display_name":"Characteristic polynomial","score":0.6923458576202393},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6569980978965759},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.6561446189880371},{"id":"https://openalex.org/keywords/companion-matrix","display_name":"Companion matrix","score":0.6137611865997314},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5672399997711182},{"id":"https://openalex.org/keywords/hermite-interpolation","display_name":"Hermite interpolation","score":0.5624105334281921},{"id":"https://openalex.org/keywords/barycentric-coordinate-system","display_name":"Barycentric coordinate system","score":0.528005838394165},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4988996982574463},{"id":"https://openalex.org/keywords/wilkinsons-polynomial","display_name":"Wilkinson's polynomial","score":0.48936551809310913},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.4748696982860565},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.47147443890571594},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.45535069704055786},{"id":"https://openalex.org/keywords/vandermonde-matrix","display_name":"Vandermonde matrix","score":0.44973790645599365},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42111724615097046},{"id":"https://openalex.org/keywords/lagrange-polynomial","display_name":"Lagrange polynomial","score":0.41985467076301575},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3841032385826111},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3498975336551666},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18478503823280334},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1316002905368805},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07741901278495789}],"concepts":[{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.8012923002243042},{"id":"https://openalex.org/C107775665","wikidata":"https://www.wikidata.org/wiki/Q12859399","display_name":"Properties of polynomial roots","level":4,"score":0.7363941073417664},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7085713148117065},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.6923458576202393},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6569980978965759},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.6561446189880371},{"id":"https://openalex.org/C141495983","wikidata":"https://www.wikidata.org/wiki/Q814361","display_name":"Companion matrix","level":5,"score":0.6137611865997314},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5672399997711182},{"id":"https://openalex.org/C186429297","wikidata":"https://www.wikidata.org/wiki/Q44451","display_name":"Hermite interpolation","level":3,"score":0.5624105334281921},{"id":"https://openalex.org/C128356825","wikidata":"https://www.wikidata.org/wiki/Q738422","display_name":"Barycentric coordinate system","level":2,"score":0.528005838394165},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4988996982574463},{"id":"https://openalex.org/C170907076","wikidata":"https://www.wikidata.org/wiki/Q2613931","display_name":"Wilkinson's polynomial","level":5,"score":0.48936551809310913},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.4748696982860565},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.47147443890571594},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.45535069704055786},{"id":"https://openalex.org/C55294529","wikidata":"https://www.wikidata.org/wiki/Q579544","display_name":"Vandermonde matrix","level":3,"score":0.44973790645599365},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42111724615097046},{"id":"https://openalex.org/C64208722","wikidata":"https://www.wikidata.org/wiki/Q861606","display_name":"Lagrange polynomial","level":3,"score":0.41985467076301575},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3841032385826111},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3498975336551666},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18478503823280334},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1316002905368805},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07741901278495789},{"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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2331684.2331706","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2331684.2331706","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W31505300","https://openalex.org/W598758435","https://openalex.org/W1691030868","https://openalex.org/W1967884132","https://openalex.org/W2022838696","https://openalex.org/W2036312716","https://openalex.org/W6637334786"],"related_works":["https://openalex.org/W2007066068","https://openalex.org/W2905919007","https://openalex.org/W2386881760","https://openalex.org/W2150665371","https://openalex.org/W783125614","https://openalex.org/W170171843","https://openalex.org/W2008280494","https://openalex.org/W2240282887","https://openalex.org/W2382784327","https://openalex.org/W2363840864"],"abstract_inverted_index":{"Computing":[0],"the":[1,8,21,24,46],"roots":[2,36,47],"of":[3,23,37,48],"a":[4,12,38,49],"polynomial":[5,39,50],"expressed":[6],"in":[7],"Lagrange":[9],"basis":[10,15],"or":[11],"Hermite":[13],"interpolational":[14],"can":[16],"be":[17],"reduced":[18],"to":[19],"computing":[20],"eigenvalues":[22],"corresponding":[25],"companion":[26],"matrix":[27],"[2].":[28],"The":[29],"result":[30],"we":[31],"present":[32],"here":[33],"is":[34],"that":[35],"computed":[40],"via":[41],"this":[42],"method":[43],"are":[44],"exactly":[45],"with":[51],"slightly":[52],"perturbed":[53],"coefficients.":[54]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
