{"id":"https://openalex.org/W2071145489","doi":"https://doi.org/10.1137/070681867","title":"Iterative Solution of Piecewise Linear Systems","display_name":"Iterative Solution of Piecewise Linear Systems","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2071145489","doi":"https://doi.org/10.1137/070681867","mag":"2071145489"},"language":"en","primary_location":{"id":"doi:10.1137/070681867","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070681867","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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":"https://openalex.org/A5036669637","display_name":"Luigi Brugnano","orcid":"https://orcid.org/0000-0002-6290-4107"},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Luigi Brugnano","raw_affiliation_strings":["university of Florence"],"affiliations":[{"raw_affiliation_string":"university of Florence","institution_ids":["https://openalex.org/I45084792"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023914916","display_name":"V Casulli","orcid":"https://orcid.org/0000-0002-2398-9339"},"institutions":[{"id":"https://openalex.org/I193223587","display_name":"University of Trento","ror":"https://ror.org/05trd4x28","country_code":"IT","type":"education","lineage":["https://openalex.org/I193223587"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Vincenzo Casulli","raw_affiliation_strings":["University of Trento"],"affiliations":[{"raw_affiliation_string":"University of Trento","institution_ids":["https://openalex.org/I193223587"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036669637"],"corresponding_institution_ids":["https://openalex.org/I45084792"],"apc_list":null,"apc_paid":null,"fwci":3.8159,"has_fulltext":false,"cited_by_count":107,"citation_normalized_percentile":{"value":0.93523293,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"30","issue":"1","first_page":"463","last_page":"472"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11250","display_name":"Wave and Wind Energy Systems","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9902999997138977,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8256078958511353},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7076385617256165},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.6469051837921143},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5941277146339417},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5817187428474426},{"id":"https://openalex.org/keywords/constant-function","display_name":"Constant function","score":0.5021846294403076},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.49776342511177063},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4741056561470032},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4648057222366333},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.46271654963493347},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.45606884360313416},{"id":"https://openalex.org/keywords/linear-complementarity-problem","display_name":"Linear complementarity problem","score":0.4228576719760895},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4222235679626465},{"id":"https://openalex.org/keywords/limit-point","display_name":"Limit point","score":0.417474627494812},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2786521017551422},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.22179383039474487},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08576658368110657}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8256078958511353},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7076385617256165},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.6469051837921143},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5941277146339417},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5817187428474426},{"id":"https://openalex.org/C153658351","wikidata":"https://www.wikidata.org/wiki/Q746264","display_name":"Constant function","level":3,"score":0.5021846294403076},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.49776342511177063},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4741056561470032},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4648057222366333},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.46271654963493347},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.45606884360313416},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.4228576719760895},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4222235679626465},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.417474627494812},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2786521017551422},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.22179383039474487},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08576658368110657},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/070681867","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070681867","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.497.4975","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.497.4975","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.math.unifi.it/users/brugnano/preprint/SISC.pdf","raw_type":"text"},{"id":"pmh:oai:flore.unifi.it:2158/313360","is_oa":false,"landing_page_url":"http://hdl.handle.net/2158/313360","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.unitn.it:11572/46894","is_oa":false,"landing_page_url":"http://hdl.handle.net/11572/46894","pdf_url":null,"source":{"id":"https://openalex.org/S4306401913","display_name":"Institutional Research Information System (Universit\u00e0 degli Studi di Trento)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I193223587","host_organization_name":"University of Trento","host_organization_lineage":["https://openalex.org/I193223587"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Clean water and sanitation","score":0.8299999833106995,"id":"https://metadata.un.org/sdg/6"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W584634945","https://openalex.org/W1488435683","https://openalex.org/W1506342804","https://openalex.org/W1512127157","https://openalex.org/W1518039036","https://openalex.org/W1981488665","https://openalex.org/W1992688650","https://openalex.org/W2000151369","https://openalex.org/W2020863487","https://openalex.org/W2021664750","https://openalex.org/W2022575150","https://openalex.org/W2035345211","https://openalex.org/W2071563913","https://openalex.org/W2073041688","https://openalex.org/W2089649903","https://openalex.org/W2090689930","https://openalex.org/W2113734366","https://openalex.org/W2125651385","https://openalex.org/W2911789798","https://openalex.org/W2914714640","https://openalex.org/W4248555053"],"related_works":["https://openalex.org/W2050897335","https://openalex.org/W3087523251","https://openalex.org/W2581624899","https://openalex.org/W4200408943","https://openalex.org/W2100864966","https://openalex.org/W2188855303","https://openalex.org/W1992855575","https://openalex.org/W2754997651","https://openalex.org/W2126954301","https://openalex.org/W4296403393"],"abstract_inverted_index":{"The":[0,42],"correct":[1],"formulation":[2],"of":[3,13,25,37,91,95,135],"numerical":[4,148],"models":[5],"for":[6,61,105],"free-surface":[7],"hydrodynamics":[8],"often":[9],"requires":[10],"the":[11,26,35,82,89,98,128],"solution":[12,27,84,130],"special":[14],"linear":[15,45,51,108],"systems":[16,46,109],"whose":[17,54],"coefficient":[18],"matrix":[19],"is":[20,85,110,116],"a":[21,70,101,120,132,146],"piecewise":[22,44,107],"constant":[23],"function":[24],"itself.":[28],"In":[29,97],"so":[30],"doing":[31],"one":[32],"may":[33,68],"prevent":[34],"development":[36],"unrealistic":[38],"negative":[39],"water":[40],"depths.":[41],"resulting":[43],"are":[47,76],"equivalent":[48],"to":[49,81,118,127],"particular":[50],"complementarity":[52],"problems":[53],"solutions":[55],"could":[56],"be":[57],"obtained":[58],"by":[59,145],"using,":[60],"example,":[62],"interior":[63],"point":[64],"methods.":[65],"These":[66],"methods":[67],"have":[69,119],"favorable":[71],"convergence":[72,80],"property,":[73,123],"but":[74],"they":[75],"purely":[77],"iterative":[78],"and":[79,112],"exact":[83,129],"proven":[86],"only":[87],"in":[88,131],"limit":[90],"an":[92],"infinite":[93],"number":[94,134],"iterations.":[96],"present":[99],"paper":[100],"simple":[102],"Newton-type":[103],"procedure":[104,115],"certain":[106],"derived":[111],"discussed.":[113],"This":[114],"shown":[117],"finite":[121,133],"termination":[122],"i.e.,":[124],"it":[125,139],"converges":[126,140],"steps,":[136],"and,":[137],"actually,":[138],"very":[141],"quickly,":[142],"as":[143],"confirmed":[144],"few":[147],"tests.":[149]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
