{"id":"https://openalex.org/W2068403757","doi":"https://doi.org/10.1137/130906544","title":"Certified Parallelotope Continuation for One-Manifolds","display_name":"Certified Parallelotope Continuation for One-Manifolds","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2068403757","doi":"https://doi.org/10.1137/130906544","mag":"2068403757"},"language":"en","primary_location":{"id":"doi:10.1137/130906544","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130906544","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Benjamin Martin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Benjamin Martin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060692753","display_name":"Alexandre Goldsztejn","orcid":"https://orcid.org/0000-0002-6561-5888"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexandre Goldsztejn","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053935960","display_name":"Laurent Granvilliers","orcid":"https://orcid.org/0000-0003-3320-7502"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Laurent Granvilliers","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5044508529","display_name":"Christophe Jermann","orcid":"https://orcid.org/0000-0002-1383-3103"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christophe Jermann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2807,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.92117551,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"51","issue":"6","first_page":"3373","last_page":"3401"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.8378999829292297,"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":0.8378999829292297,"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":0.053599998354911804,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.02280000038444996,"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/mathematics","display_name":"Mathematics","score":0.682319700717926},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.6287268996238708},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6078834533691406},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.6058899164199829},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.5247756838798523},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.51175856590271},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48787522315979004},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.45416149497032166},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42059844732284546},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36374974250793457},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33656781911849976},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28602373600006104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25405415892601013},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.18614345788955688},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.0918281078338623}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.682319700717926},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6287268996238708},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6078834533691406},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.6058899164199829},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.5247756838798523},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.51175856590271},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48787522315979004},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.45416149497032166},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42059844732284546},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36374974250793457},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33656781911849976},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28602373600006104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25405415892601013},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.18614345788955688},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0918281078338623},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/130906544","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130906544","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:HAL:hal-01408525v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01408525","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, 2013, 51 (6), pp.3373-3401","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W53809769","https://openalex.org/W122692412","https://openalex.org/W1606015457","https://openalex.org/W1974585479","https://openalex.org/W1989690536","https://openalex.org/W1989818977","https://openalex.org/W2009334861","https://openalex.org/W2015441000","https://openalex.org/W2022723352","https://openalex.org/W2049665423","https://openalex.org/W2057641327","https://openalex.org/W2064311953","https://openalex.org/W2067783185","https://openalex.org/W2069255158","https://openalex.org/W2073787328","https://openalex.org/W2113023083","https://openalex.org/W2129041497","https://openalex.org/W2156656541","https://openalex.org/W2169004268","https://openalex.org/W4213171111","https://openalex.org/W4298841221"],"related_works":["https://openalex.org/W2520934858","https://openalex.org/W2098412892","https://openalex.org/W2990487117","https://openalex.org/W43877154","https://openalex.org/W109635080","https://openalex.org/W4213384165","https://openalex.org/W2377262226","https://openalex.org/W2531534085","https://openalex.org/W4285295794","https://openalex.org/W34401233"],"abstract_inverted_index":{"Starting":[0],"from":[1,36,67],"an":[2,23],"initial":[3],"solution,":[4],"continuation":[5,110,195],"methods":[6,46,91],"efficiently":[7],"produce":[8],"a":[9,14,30,105,188,193],"sequence":[10],"of":[11,22,26,33,60,142,146,157,182],"points":[12,52],"on":[13,84,93,96,113],"manifold":[15],"typically":[16],"defined":[17,127],"as":[18,126,197],"the":[19,50,56,61,85,97,120,158,169,179,183],"solution":[20],"set":[21],"underconstrained":[24],"system":[25],"equations.":[27],"They":[28],"have":[29],"wide":[31],"range":[32],"applications":[34],"ranging":[35],"curve":[37,185],"plotting":[38],"to":[39,55,70,73,80,89,153,178],"polynomial":[40],"root-finding":[41],"by":[42,199],"homotopy.":[43],"However,":[44],"classical":[45],"cannot":[47],"guarantee":[48],"that":[49,122,171],"returned":[51],"all":[53],"belong":[54],"same":[57],"connected":[58],"component":[59,69],"manifold,":[62],"i.e.,":[63],"they":[64],"may":[65],"jump":[66],"one":[68,86],"another.":[71],"Trying":[72],"overcome":[74],"this":[75,101],"issue":[76],"has":[77],"given":[78],"birth":[79],"several":[81],"sophisticated":[82],"heuristics":[83],"hand":[87],"and":[88,131,139],"guaranteed":[90],"based":[92,112],"rigorous":[94,107],"computations":[95],"other":[98],"hand.":[99],"In":[100],"paper":[102],"we":[103],"introduce":[104],"new":[106,135],"predictor":[108],"corrector":[109],"method":[111],"interval":[114,167],"computations.":[115],"Its":[116],"novelty":[117],"lies":[118],"in":[119,128],"fact":[121,170],"it":[123],"uses":[124],"parallelotopes":[125,187],"A.":[129],"Goldsztejn":[130],"L.":[132],"Granvilliers,":[133],"A":[134],"framework":[136],"for":[137,192],"sharp":[138],"efficient":[140],"resolution":[141],"NCSP":[143],"with":[144],"manifolds":[145],"solutions,":[147],"Constraints,":[148],"15":[149],"(2010),":[150],"pp.":[151],"190--212,":[152],"enclose":[154],"consecutive":[155],"portions":[156],"followed":[159,184],"manifold.":[160],"Though":[161],"computationally":[162],"more":[163],"expensive":[164],"than":[165],"regular":[166],"computations,":[168],"their":[172],"orientation":[173],"can":[174],"be":[175],"automatically":[176],"adapted":[177],"local":[180],"topology":[181],"makes":[186],"very":[189],"suitable":[190],"tool":[191],"certified":[194],"method,":[196],"shown":[198],"reported":[200],"experimental":[201],"results.":[202]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}