{"id":"https://openalex.org/W2054373049","doi":"https://doi.org/10.1137/060650295","title":"Rigidity in Finite-Element Matrices: Sufficient Conditions for the Rigidity of Structures and Substructures","display_name":"Rigidity in Finite-Element Matrices: Sufficient Conditions for the Rigidity of Structures and Substructures","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2054373049","doi":"https://doi.org/10.1137/060650295","mag":"2054373049"},"language":"en","primary_location":{"id":"doi:10.1137/060650295","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060650295","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5047493306","display_name":"Gil Shklarski","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gil Shklarski","raw_affiliation_strings":["shagil@tau.ac.il#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"shagil@tau.ac.il#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056808449","display_name":"Sivan Toledo","orcid":"https://orcid.org/0000-0002-9524-7115"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sivan Toledo","raw_affiliation_strings":["stoledo@tau.ac.il#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"stoledo@tau.ac.il#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.8965,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.94122162,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"30","issue":"1","first_page":"7","last_page":"40"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11870","display_name":"Structural Analysis and Optimization","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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/T11870","display_name":"Structural Analysis and Optimization","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T11737","display_name":"Advanced Materials and Mechanics","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9945999979972839,"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/finite-element-method","display_name":"Finite element method","score":0.8101803064346313},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7751023173332214},{"id":"https://openalex.org/keywords/rigidity","display_name":"Rigidity (electromagnetism)","score":0.7145463228225708},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4712139666080475},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.401577353477478},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3535583019256592},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3264385461807251}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.8101803064346313},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7751023173332214},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.7145463228225708},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4712139666080475},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.401577353477478},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3535583019256592},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3264385461807251},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/060650295","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060650295","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.64.9503","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.64.9503","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.tau.ac.il/~stoledo/Pubs/rigidity.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W100944330","https://openalex.org/W1487775490","https://openalex.org/W1530008367","https://openalex.org/W1567467079","https://openalex.org/W1587744656","https://openalex.org/W1977438424","https://openalex.org/W1993111701","https://openalex.org/W2004283384","https://openalex.org/W2053416790","https://openalex.org/W2066052393","https://openalex.org/W2073772681","https://openalex.org/W2077791079","https://openalex.org/W2088062469","https://openalex.org/W2090129250","https://openalex.org/W2113679823","https://openalex.org/W2121403868","https://openalex.org/W2139834426","https://openalex.org/W2172211108","https://openalex.org/W3119976028","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W1971388572","https://openalex.org/W2370926798","https://openalex.org/W2793786119","https://openalex.org/W4234142113","https://openalex.org/W3145389907"],"abstract_inverted_index":{"We":[0,42,55,71],"present":[1,44],"an":[2],"algebraic":[3,15],"theory":[4,11,105,139],"of":[5,17,21,23,27,115,124,165],"rigidity":[6,22,29,38],"for":[7,37,52,79,100],"finite-element":[8,18,24,53,101,116,122],"matrices.":[9,54,102],"The":[10],"provides":[12],"a":[13,45,112],"formal":[14],"definition":[16],"matrices;":[19,33],"notions":[20],"matrices":[25,62,83,119,151],"and":[26,34,39,106,127,134,140,152,161],"mutual":[28,40],"between":[30],"two":[31],"such":[32],"sufficient":[35],"conditions":[36],"rigidity.":[41],"also":[43,72],"novel":[46],"sparsification":[47,59],"technique,":[48],"called":[49],"fretsaw":[50,80],"extension,":[51],"show":[56,73],"that":[57,63,74,84],"this":[58],"technique":[60],"generates":[61,82],"are":[64,109,143,153],"mutually":[65],"rigid":[66],"with":[67,88],"the":[68,138,141,149,156,158,162,166],"original":[69],"matrix.":[70],"one":[75],"particular":[76],"construction":[77],"algorithm":[78,93],"extensions":[81],"can":[85,94],"be":[86,95],"factored":[87],"essentially":[89],"no":[90],"fill.":[91],"This":[92],"used":[96],"to":[97,111,155],"construct":[98],"preconditioners":[99],"Both":[103,137],"our":[104,107],"algorithms":[108,142],"applicable":[110],"wide":[113],"range":[114],"matrices,":[117],"including":[118],"arising":[120],"from":[121],"discretizations":[123],"both":[125],"scalar":[126],"vector":[128],"partial":[129],"differential":[130],"equations":[131],"(e.g.,":[132],"electrostatics":[133],"linear":[135],"elasticity).":[136],"purely":[144],"algebraic-combinatorial.":[145],"They":[146],"manipulate":[147],"only":[148],"element":[150],"oblivious":[154],"geometry,":[157],"material":[159],"properties,":[160],"discretization":[163],"details":[164],"underlying":[167],"continuous":[168],"problem.":[169]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}