{"id":"https://openalex.org/W2007088323","doi":"https://doi.org/10.1137/130932387","title":"Numerical Solution of Bivariate and Polyanalytic Polynomial Systems","display_name":"Numerical Solution of Bivariate and Polyanalytic Polynomial Systems","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2007088323","doi":"https://doi.org/10.1137/130932387","mag":"2007088323"},"language":"en","primary_location":{"id":"doi:10.1137/130932387","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130932387","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://lirias.kuleuven.be/handle/123456789/452484","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029774694","display_name":"Laurent Sorber","orcid":null},"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":true,"raw_author_name":"Laurent Sorber","raw_affiliation_strings":["Katholieke Universiteit \u00adLeuven"],"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit \u00adLeuven","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052654029","display_name":"Marc Van Barel","orcid":"https://orcid.org/0000-0002-7372-382X"},"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":"Marc Van Barel","raw_affiliation_strings":["Katholieke Universiteit \u00adLeuven"],"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit \u00adLeuven","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009006026","display_name":"Lieven De Lathauwer","orcid":"https://orcid.org/0000-0001-5562-5014"},"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":"Lieven De Lathauwer","raw_affiliation_strings":["Katholieke Universiteit \u00adLeuven"],"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit \u00adLeuven","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5029774694"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":3.2047,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.91695203,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"52","issue":"4","first_page":"1551","last_page":"1572"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9998000264167786,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9947999715805054,"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/mathematics","display_name":"Mathematics","score":0.7432540655136108},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.6888348460197449},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6096428632736206},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5102002620697021},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46520453691482544},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44363972544670105},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3679136633872986},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22257503867149353}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7432540655136108},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.6888348460197449},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6096428632736206},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5102002620697021},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46520453691482544},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44363972544670105},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3679136633872986},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22257503867149353},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/130932387","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130932387","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/452484","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/452484","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"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":"SIAM Journal on Numerical Analysis, vol. 52 (4), (1551-1572)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/452484","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/452484","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"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":"SIAM Journal on Numerical Analysis, vol. 52 (4), (1551-1572)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W45149845","https://openalex.org/W303777154","https://openalex.org/W647818151","https://openalex.org/W1481556851","https://openalex.org/W1570420806","https://openalex.org/W1574151794","https://openalex.org/W1579224486","https://openalex.org/W1580809199","https://openalex.org/W1702387807","https://openalex.org/W1963826206","https://openalex.org/W1966047467","https://openalex.org/W1967344706","https://openalex.org/W1968297701","https://openalex.org/W1976682447","https://openalex.org/W1982227707","https://openalex.org/W1985548249","https://openalex.org/W2000215628","https://openalex.org/W2006948763","https://openalex.org/W2007715285","https://openalex.org/W2010761584","https://openalex.org/W2011353123","https://openalex.org/W2011693299","https://openalex.org/W2019127701","https://openalex.org/W2024165284","https://openalex.org/W2025485823","https://openalex.org/W2028576930","https://openalex.org/W2029122069","https://openalex.org/W2030143626","https://openalex.org/W2034955763","https://openalex.org/W2038345254","https://openalex.org/W2040006659","https://openalex.org/W2042650700","https://openalex.org/W2043938310","https://openalex.org/W2044080186","https://openalex.org/W2049087128","https://openalex.org/W2055909024","https://openalex.org/W2077223725","https://openalex.org/W2077961479","https://openalex.org/W2079639858","https://openalex.org/W2093721325","https://openalex.org/W2114144879","https://openalex.org/W2117948699","https://openalex.org/W2119842211","https://openalex.org/W2120467997","https://openalex.org/W2121739212","https://openalex.org/W2130952444","https://openalex.org/W2133404041","https://openalex.org/W2134977872","https://openalex.org/W2149454052","https://openalex.org/W2159503542","https://openalex.org/W2162438491","https://openalex.org/W2170485468","https://openalex.org/W2239344586","https://openalex.org/W3029645440","https://openalex.org/W4251856170"],"related_works":["https://openalex.org/W3099337062","https://openalex.org/W755632419","https://openalex.org/W2096369821","https://openalex.org/W2225037421","https://openalex.org/W2083903569","https://openalex.org/W2950834363","https://openalex.org/W2315030772","https://openalex.org/W2352964114","https://openalex.org/W2742228879","https://openalex.org/W2359191660"],"abstract_inverted_index":{"Finding":[0],"the":[1,51,75,95,98,103,128,141],"real":[2,99],"solutions":[3,137],"of":[4,118,136],"a":[5,10,40,90,133],"bivariate":[6,34,80],"polynomial":[7,37],"system":[8],"is":[9,114,139],"central":[11],"problem":[12],"in":[13,89],"robotics,":[14],"computer":[15],"modeling":[16],"and":[17,21,28,35,85,111,121,138,146],"graphics,":[18],"computational":[19],"geometry,":[20],"numerical":[22,119],"optimization.":[23],"We":[24],"propose":[25],"an":[26],"efficient":[27],"numerically":[29],"robust":[30],"algorithm":[31,53,130],"for":[32],"solving":[33,70],"polyanalytic":[36,83],"systems":[38,81,84],"using":[39],"single":[41],"generalized":[42],"eigenvalue":[43],"decomposition.":[44],"In":[45],"contrast":[46],"to":[47,73,93],"existing":[48],"eigen-based":[49],"solvers,":[50],"proposed":[52,129],"does":[54,64],"not":[55],"depend":[56],"on":[57],"Gr\u00f6bner":[58],"bases":[59],"or":[60,69],"normal":[61],"sets,":[62],"nor":[63],"it":[65],"require":[66],"computing":[67],"eigenvectors":[68],"additional":[71],"eigenproblems":[72],"recover":[74],"solution.":[76],"The":[77],"method":[78],"transforms":[79],"into":[82],"then":[86],"uses":[87],"resultants":[88],"novel":[91],"way":[92],"project":[94],"variables":[96],"onto":[97],"plane":[100],"associated":[101],"with":[102],"two":[104],"variables.":[105],"Solutions":[106],"are":[107],"returned":[108],"counting":[109],"multiplicity":[110],"their":[112],"accuracy":[113],"maximized":[115],"by":[116],"means":[117],"balancing":[120],"Newton--Raphson":[122],"refinement.":[123],"Numerical":[124],"experiments":[125],"show":[126],"that":[127],"consistently":[131],"recovers":[132],"higher":[134],"percentage":[135],"at":[140],"same":[142],"time":[143],"significantly":[144],"faster":[145],"more":[147],"accurate":[148],"than":[149],"competing":[150],"double":[151],"precision":[152],"solvers.":[153]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}