{"id":"https://openalex.org/W4405907290","doi":"https://doi.org/10.1051/ro/2024234","title":"Accelerated derivative-free spectral residual method for nonlinear systems of equations","display_name":"Accelerated derivative-free spectral residual method for nonlinear systems of equations","publication_year":2024,"publication_date":"2024-12-30","ids":{"openalex":"https://openalex.org/W4405907290","doi":"https://doi.org/10.1051/ro/2024234"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2024234","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2024234","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2025/01/ro240062.pdf","source":{"id":"https://openalex.org/S4393919633","display_name":"RAIRO. Operations research","issn_l":"2804-7303","issn":["2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.rairo-ro.org/articles/ro/pdf/2025/01/ro240062.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087290455","display_name":"Ernesto G. Birgin","orcid":"https://orcid.org/0000-0002-7466-7663"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Ernesto G. Birgin","raw_affiliation_strings":["Department of Computer Science, Institute of Mathematics and Statistics, University of S\u00e3o Paulo, S\u00e3o Paulo, SP, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-7466-7663","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Institute of Mathematics and Statistics, University of S\u00e3o Paulo, S\u00e3o Paulo, SP, Brazil","institution_ids":["https://openalex.org/I17974374"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028651017","display_name":"John Lenon Cardoso Gardenghi","orcid":"https://orcid.org/0000-0003-4443-8090"},"institutions":[{"id":"https://openalex.org/I150729083","display_name":"Universidade de Bras\u00edlia","ror":"https://ror.org/02xfp8v59","country_code":"BR","type":"education","lineage":["https://openalex.org/I150729083"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"John L. Gardenghi","raw_affiliation_strings":["Faculty of Sciences and Technologies in Engineering, University of Bras\u00edlia, Bras\u00edlia, DF, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Sciences and Technologies in Engineering, University of Bras\u00edlia, Bras\u00edlia, DF, Brazil","institution_ids":["https://openalex.org/I150729083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077449995","display_name":"D. S. Marcondes","orcid":"https://orcid.org/0000-0002-8189-8734"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Diaulas S. Marcondes","raw_affiliation_strings":["Department of Applied Mathematics, Institute of Mathematics and Statistics, University of S\u00e3o Paulo, S\u00e3o Paulo, SP, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Institute of Mathematics and Statistics, University of S\u00e3o Paulo, S\u00e3o Paulo, SP, Brazil","institution_ids":["https://openalex.org/I17974374"]}]},{"author_position":"last","author":{"id":null,"display_name":"Jos\u00e9 Mario Mart\u00ednez","orcid":null},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 Mario Mart\u00ednez","raw_affiliation_strings":["Department of Applied Mathematics, Institute of Mathematics, Statistics and Scientific Computing, State University of Campinas, Campinas, SP, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Institute of Mathematics, Statistics and Scientific Computing, State University of Campinas, Campinas, SP, Brazil","institution_ids":["https://openalex.org/I181391015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.36182694,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"59","issue":"1","first_page":"609","last_page":"624"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9883999824523926,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9883999824523926,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9703999757766724,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9424999952316284,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/nonlinear-system","display_name":"Nonlinear system","score":0.7762714624404907},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6895259618759155},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.638878583908081},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.601949155330658},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5727419257164001},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4974565804004669},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47601205110549927},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.47124940156936646},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.458712637424469},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.45130455493927},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3758561313152313},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35601890087127686},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2902544140815735},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16269156336784363}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7762714624404907},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6895259618759155},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.638878583908081},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.601949155330658},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5727419257164001},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4974565804004669},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47601205110549927},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.47124940156936646},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.458712637424469},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.45130455493927},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3758561313152313},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35601890087127686},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2902544140815735},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16269156336784363},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ro/2024234","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2024234","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2025/01/ro240062.pdf","source":{"id":"https://openalex.org/S4393919633","display_name":"RAIRO. Operations research","issn_l":"2804-7303","issn":["2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:repositorio.unb.br:10482/51889","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2024234.","pdf_url":null,"source":{"id":"https://openalex.org/S4377196379","display_name":"RIUnB Institutional Repository (University of Bras\u00edlia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I150729083","host_organization_name":"Universidade de Bras\u00edlia","host_organization_lineage":["https://openalex.org/I150729083"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"instacron:UNB","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1051/ro/2024234","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ro/2024234","pdf_url":"https://www.rairo-ro.org/articles/ro/pdf/2025/01/ro240062.pdf","source":{"id":"https://openalex.org/S4393919633","display_name":"RAIRO. Operations research","issn_l":"2804-7303","issn":["2804-7303"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1131776356","display_name":null,"funder_award_id":"2023/08706-1","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G1158688722","display_name":null,"funder_award_id":"302538/2019","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G2253547418","display_name":null,"funder_award_id":"2013/07375-0, 2022/05803-3, and 2023/08706-1","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G2363588307","display_name":null,"funder_award_id":"302073/2022-1","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G2486662831","display_name":null,"funder_award_id":"2013/07375-","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G3865329954","display_name":null,"funder_award_id":"302073/2022-1 and 302538/2019- 4","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G5990746028","display_name":null,"funder_award_id":"2013/07375-0","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G6132555478","display_name":null,"funder_award_id":"2022/05803-3","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G6669552033","display_name":null,"funder_award_id":"2013/07375-0","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G7292133820","display_name":null,"funder_award_id":"302538/2019-4","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405907290.pdf","grobid_xml":"https://content.openalex.org/works/W4405907290.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1748199557","https://openalex.org/W1973734200","https://openalex.org/W1978100686","https://openalex.org/W2000359198","https://openalex.org/W2012341322","https://openalex.org/W2012564502","https://openalex.org/W2024490641","https://openalex.org/W2050096287","https://openalex.org/W2056603712","https://openalex.org/W2057565823","https://openalex.org/W2068484625","https://openalex.org/W2074809615","https://openalex.org/W2076605490","https://openalex.org/W2102790339","https://openalex.org/W2149454052","https://openalex.org/W2160332416","https://openalex.org/W2165644087","https://openalex.org/W2166308223","https://openalex.org/W2485779782","https://openalex.org/W4206097460","https://openalex.org/W4240022917","https://openalex.org/W4252894371","https://openalex.org/W4298068286","https://openalex.org/W4313232682"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W4293683879","https://openalex.org/W2253637996","https://openalex.org/W4388482258","https://openalex.org/W288746350","https://openalex.org/W1550587116","https://openalex.org/W2118018204","https://openalex.org/W2212647145","https://openalex.org/W2402673101"],"abstract_inverted_index":{"Many":[0],"continuous":[1],"models":[2],"of":[3,9,13,19,36,68,114,142,173,204,215],"natural":[4],"phenomena":[5],"require":[6],"the":[7,17,34,96,108,115,128,143,151,166,171,178,192,213],"solution":[8,35],"large-scale":[10],"nonlinear":[11,41,66,160,201],"systems":[12,67],"equations.":[14],"For":[15],"example,":[16],"discretization":[18],"many":[20],"partial":[21],"differential":[22],"equations,":[23],"which":[24,39,51,196],"are":[25,56,61],"widely":[26,123],"used":[27,124],"in":[28,38,50,177],"physics,":[29],"chemistry,":[30],"and":[31,77,105,191,207],"engineering,":[32],"requires":[33],"subproblems":[37],"a":[40,73,122,156,183,199,209],"algebraic":[42],"system":[43],"has":[44],"to":[45],"be":[46],"addressed,":[47],"especially":[48],"one":[49],"stable":[52],"implicit":[53],"difference":[54],"schemes":[55],"used.":[57],"Spectral":[58],"residual":[59],"methods":[60],"powerful":[62],"tools":[63],"for":[64,159,211],"solving":[65],"equations":[69],"without":[70],"derivatives.":[71],"In":[72,107],"recent":[74],"paper":[75],"[Birgin":[76],"Mart\u00ednez,":[78],"SIAM":[79],"J.":[80],"Numer.":[81],"Anal":[82],".":[83],"60":[84],"(2022)":[85],"3145\u20133180],":[86],"it":[87],"was":[88],"shown":[89],"that":[90,139,165],"an":[91,111,185],"acceleration":[92,167],"technique":[93],"based":[94],"on":[95],"Sequential":[97],"Secant":[98],"Method":[99],"can":[100],"greatly":[101,169],"improve":[102],"its":[103,132,174],"efficiency":[104],"robustness.":[106],"present":[109],"work,":[110],"R":[112,144,180,190],"implementation":[113],"method":[116,153],"is":[117,140,187],"presented.":[118],"Numerical":[119],"experiments":[120,149],"with":[121,131,154],"test":[125],"bed":[126],"compare":[127,150],"presented":[129],"approach":[130],"plain":[133],"(":[134],"i.e":[135],".,":[136],"non-accelerated)":[137],"version":[138],"part":[141],"package":[145],"BB.":[146],"Additional":[147],"numerical":[148],"proposed":[152],"NITSOL,":[155],"state-of-the-art":[157],"solver":[158],"systems.":[161],"These":[162],"comparisons":[163],"show":[164],"process":[168],"improves":[170],"robustness":[172],"counterpart":[175],"included":[176],"existing":[179],"package.":[181],"As":[182],"by-product,":[184],"interface":[186],"provided":[188],"between":[189],"consolidated":[193],"CUTEst":[194],"collection,":[195],"contains":[197],"over":[198],"thousand":[200],"programming":[202],"problems":[203],"all":[205],"types":[206],"represents":[208],"standard":[210],"evaluating":[212],"performance":[214],"optimization":[216],"methods.":[217]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}