{"id":"https://openalex.org/W1973718105","doi":"https://doi.org/10.1155/2013/732834","title":"The Preconditioned SOR Iterative Method for Positive Definite Matrices","display_name":"The Preconditioned SOR Iterative Method for Positive Definite Matrices","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1973718105","doi":"https://doi.org/10.1155/2013/732834","mag":"1973718105"},"language":"en","primary_location":{"id":"doi:10.1155/2013/732834","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/732834","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/732834.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2013/732834.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103706516","display_name":"Yuqin Bai","orcid":null},"institutions":[{"id":"https://openalex.org/I124644866","display_name":"Northwest Minzu University","ror":"https://ror.org/04cyy9943","country_code":"CN","type":"education","lineage":["https://openalex.org/I124644866"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yu-Qin Bai","raw_affiliation_strings":["School of Computer Science and Information Engineering, Northwest University for Nationalities, Lanzhou, Gansu 730030, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Information Engineering, Northwest University for Nationalities, Lanzhou, Gansu 730030, China","institution_ids":["https://openalex.org/I124644866"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114153374","display_name":"Yanping Xiao","orcid":null},"institutions":[{"id":"https://openalex.org/I124644866","display_name":"Northwest Minzu University","ror":"https://ror.org/04cyy9943","country_code":"CN","type":"education","lineage":["https://openalex.org/I124644866"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan-Ping Xiao","raw_affiliation_strings":["School of Computer Science and Information Engineering, Northwest University for Nationalities, Lanzhou, Gansu 730030, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Information Engineering, Northwest University for Nationalities, Lanzhou, Gansu 730030, China","institution_ids":["https://openalex.org/I124644866"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004121282","display_name":"Weiyuan Ma","orcid":"https://orcid.org/0000-0002-4724-2774"},"institutions":[{"id":"https://openalex.org/I124644866","display_name":"Northwest Minzu University","ror":"https://ror.org/04cyy9943","country_code":"CN","type":"education","lineage":["https://openalex.org/I124644866"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei-Yuan Ma","raw_affiliation_strings":["School of Computer Science and Information Engineering, Northwest University for Nationalities, Lanzhou, Gansu 730030, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Information Engineering, Northwest University for Nationalities, Lanzhou, Gansu 730030, China","institution_ids":["https://openalex.org/I124644866"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5103706516"],"corresponding_institution_ids":["https://openalex.org/I124644866"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.06099592,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"4"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9970999956130981,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.8745232224464417},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7231889963150024},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6393440365791321},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6039758324623108},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.5513831377029419},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5324566960334778},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.519249677658081},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.29371896386146545},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06048429012298584}],"concepts":[{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.8745232224464417},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7231889963150024},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6393440365791321},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6039758324623108},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.5513831377029419},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5324566960334778},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.519249677658081},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29371896386146545},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06048429012298584},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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:10.1155/2013/732834","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/732834","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/732834.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394808133","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394808133","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:732834","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/732834.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:892f9718b3cc42299269566f16e5dc20","is_oa":true,"landing_page_url":"https://doaj.org/article/892f9718b3cc42299269566f16e5dc20","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/732834","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/732834","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/732834.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.49000000953674316,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1544863199","display_name":null,"funder_award_id":"31920130005","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3052564992","display_name":null,"funder_award_id":"11161041","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G811115538","display_name":null,"funder_award_id":"71301111","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1973718105.pdf","grobid_xml":"https://content.openalex.org/works/W1973718105.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1972727112","https://openalex.org/W1977767016","https://openalex.org/W2011003221","https://openalex.org/W2015112325","https://openalex.org/W2015277714","https://openalex.org/W2082016411","https://openalex.org/W2127032907","https://openalex.org/W4239359156"],"related_works":["https://openalex.org/W1719857135","https://openalex.org/W2083626174","https://openalex.org/W2358921742","https://openalex.org/W2236654713","https://openalex.org/W2383395740","https://openalex.org/W2029431083","https://openalex.org/W2535168603","https://openalex.org/W2394000971","https://openalex.org/W1844423250","https://openalex.org/W4205335745"],"abstract_inverted_index":{"We":[0],"present":[1],"several":[2],"iterations":[3],"for":[4,19],"preconditioners":[5],"introduced":[6],"by":[7],"Tarazaga":[8],"and":[9,12,31],"Cuellar":[10],"(2009),":[11],"study":[13],"the":[14,17,41],"convergence":[15],"of":[16],"method":[18],"solving":[20],"a":[21],"linear":[22],"system":[23],"whose":[24],"coefficient":[25],"matrix":[26],"is":[27,45],"positive":[28],"definite":[29],"matrices,":[30],"we":[32],"also":[33],"find":[34],"that":[35],"they":[36],"complete":[37],"very":[38],"well":[39],"with":[40],"SOR":[42],"iteration,":[43],"which":[44],"shown":[46],"through":[47],"numerical":[48],"examples.":[49]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}