{"id":"https://openalex.org/W2089719986","doi":"https://doi.org/10.1080/00207160701458245","title":"Solving a non-smooth eigenvalue problem using operator-splitting methods","display_name":"Solving a non-smooth eigenvalue problem using operator-splitting methods","publication_year":2007,"publication_date":"2007-06-01","ids":{"openalex":"https://openalex.org/W2089719986","doi":"https://doi.org/10.1080/00207160701458245","mag":"2089719986"},"language":"en","primary_location":{"id":"doi:10.1080/00207160701458245","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701458245","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5049225725","display_name":"Kirsi Majava","orcid":null},"institutions":[{"id":"https://openalex.org/I1323252656","display_name":"Information Technology University","ror":"https://ror.org/00ngv8j44","country_code":"PK","type":"education","lineage":["https://openalex.org/I1323252656"]},{"id":"https://openalex.org/I94722563","display_name":"University of Jyv\u00e4skyl\u00e4","ror":"https://ror.org/05n3dz165","country_code":"FI","type":"education","lineage":["https://openalex.org/I94722563"]}],"countries":["FI","PK"],"is_corresponding":true,"raw_author_name":"K. Majava","raw_affiliation_strings":["University of Jyv\u00e4skyl\u00e4, Department of Mathematical Information Technology , P.O. Box 35 (Agora), FIN-40014 University of Jyv\u00e4skyl\u00e4, Finland","[Department of Mathematical Information Technology, University of Jyv\u00e4skyl\u00e4 Finland]"],"affiliations":[{"raw_affiliation_string":"University of Jyv\u00e4skyl\u00e4, Department of Mathematical Information Technology , P.O. Box 35 (Agora), FIN-40014 University of Jyv\u00e4skyl\u00e4, Finland","institution_ids":["https://openalex.org/I94722563"]},{"raw_affiliation_string":"[Department of Mathematical Information Technology, University of Jyv\u00e4skyl\u00e4 Finland]","institution_ids":["https://openalex.org/I1323252656"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056887719","display_name":"Roland Glowinski","orcid":null},"institutions":[{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. Glowinski","raw_affiliation_strings":["University of Houston, Department of Mathematics , 651 Hoffman Hall, Houston, TX, 77204-3008, USA","Department of Mathematics, University of Houston Houston, TX, USA"],"affiliations":[{"raw_affiliation_string":"University of Houston, Department of Mathematics , 651 Hoffman Hall, Houston, TX, 77204-3008, USA","institution_ids":["https://openalex.org/I44461941"]},{"raw_affiliation_string":"Department of Mathematics, University of Houston Houston, TX, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056914205","display_name":"Tommi K\u00e4rkk\u00e4inen","orcid":"https://orcid.org/0000-0003-0327-1167"},"institutions":[{"id":"https://openalex.org/I1323252656","display_name":"Information Technology University","ror":"https://ror.org/00ngv8j44","country_code":"PK","type":"education","lineage":["https://openalex.org/I1323252656"]},{"id":"https://openalex.org/I94722563","display_name":"University of Jyv\u00e4skyl\u00e4","ror":"https://ror.org/05n3dz165","country_code":"FI","type":"education","lineage":["https://openalex.org/I94722563"]}],"countries":["FI","PK"],"is_corresponding":false,"raw_author_name":"T. K\u00e4rkk\u00e4inen","raw_affiliation_strings":["University of Jyv\u00e4skyl\u00e4, Department of Mathematical Information Technology , P.O. Box 35 (Agora), FIN-40014 University of Jyv\u00e4skyl\u00e4, Finland","[Department of Mathematical Information Technology, University of Jyv\u00e4skyl\u00e4 Finland]"],"affiliations":[{"raw_affiliation_string":"University of Jyv\u00e4skyl\u00e4, Department of Mathematical Information Technology , P.O. Box 35 (Agora), FIN-40014 University of Jyv\u00e4skyl\u00e4, Finland","institution_ids":["https://openalex.org/I94722563"]},{"raw_affiliation_string":"[Department of Mathematical Information Technology, University of Jyv\u00e4skyl\u00e4 Finland]","institution_ids":["https://openalex.org/I1323252656"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5049225725"],"corresponding_institution_ids":["https://openalex.org/I1323252656","https://openalex.org/I94722563"],"apc_list":null,"apc_paid":null,"fwci":1.0929,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.7844437,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"84","issue":"6","first_page":"825","last_page":"846"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998999834060669,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7635294198989868},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7043579816818237},{"id":"https://openalex.org/keywords/operator-splitting","display_name":"Operator splitting","score":0.6578499674797058},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.6084997653961182},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5818169116973877},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4693357050418854},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.46345019340515137},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42752718925476074},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14706629514694214}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7635294198989868},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7043579816818237},{"id":"https://openalex.org/C2987355758","wikidata":"https://www.wikidata.org/wiki/Q25037251","display_name":"Operator splitting","level":2,"score":0.6578499674797058},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6084997653961182},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5818169116973877},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4693357050418854},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46345019340515137},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42752718925476074},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14706629514694214},{"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},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160701458245","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160701458245","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-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/W1498729261","https://openalex.org/W1551360398","https://openalex.org/W1658203550","https://openalex.org/W1967077838","https://openalex.org/W1967468633","https://openalex.org/W2002597165","https://openalex.org/W2006596837","https://openalex.org/W2022977680","https://openalex.org/W2033736734","https://openalex.org/W2049161806","https://openalex.org/W2059586807","https://openalex.org/W2061175874","https://openalex.org/W2089998388","https://openalex.org/W2099655567","https://openalex.org/W2238463638","https://openalex.org/W2568342123","https://openalex.org/W2985272081","https://openalex.org/W4292311687","https://openalex.org/W4298228534","https://openalex.org/W4301259617","https://openalex.org/W4301283118"],"related_works":["https://openalex.org/W2318982644","https://openalex.org/W1975289146","https://openalex.org/W2087240539","https://openalex.org/W2105887828","https://openalex.org/W4236520801","https://openalex.org/W2165749285","https://openalex.org/W2122599759","https://openalex.org/W412354254","https://openalex.org/W4247589295","https://openalex.org/W4379522615"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"the":[5,25,32,52],"solution":[6],"of":[7,57],"a":[8],"certain":[9],"non-smooth":[10],"eigenvalue":[11],"problem,":[12],"using":[13],"operator-splitting":[14],"methods":[15],"to":[16,48,51],"solve":[17],"an":[18],"equivalent,":[19],"constrained":[20],"minimization":[21],"problem.":[22],"We":[23],"present":[24],"Marchuk\u2013Yanenko":[26,53],"and":[27,34,59],"Peaceman\u2013Rachford":[28,44],"schemes":[29],"for":[30],"solving":[31],"problem":[33],"compare":[35],"their":[36],"performance":[37],"numerically":[38],"on":[39],"some":[40],"model":[41],"problems.":[42],"The":[43],"scheme":[45,54],"turns":[46],"out":[47],"be":[49],"superior":[50],"in":[55],"terms":[56],"accuracy":[58],"computational":[60],"efficiency.":[61]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"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"}