{"id":"https://openalex.org/W1997388431","doi":"https://doi.org/10.1155/2013/213659","title":"Block Preconditioned SSOR Methods for -Matrices Linear Systems","display_name":"Block Preconditioned SSOR Methods for -Matrices Linear Systems","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1997388431","doi":"https://doi.org/10.1155/2013/213659","mag":"1997388431"},"language":"en","primary_location":{"id":"doi:10.1155/2013/213659","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/213659","pdf_url":null,"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://doi.org/10.1155/2013/213659","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110844711","display_name":"Zhao-Nian Pu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210117818","display_name":"Hexi University","ror":"https://ror.org/02axfzt86","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210117818"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhao-Nian Pu","raw_affiliation_strings":["School of Mathematics and Statistics, Hexi University, Zhangye, Gansu 734000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Hexi University, Zhangye, Gansu 734000, China","institution_ids":["https://openalex.org/I4210117818"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039672243","display_name":"Xuezhong Wang","orcid":"https://orcid.org/0000-0001-9159-3371"},"institutions":[{"id":"https://openalex.org/I4210117818","display_name":"Hexi University","ror":"https://ror.org/02axfzt86","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210117818"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xue-Zhong Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Hexi University, Zhangye, Gansu 734000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Hexi University, Zhangye, Gansu 734000, China","institution_ids":["https://openalex.org/I4210117818"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039672243"],"corresponding_institution_ids":["https://openalex.org/I4210117818"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.07585306,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"7"},"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":0.998199999332428,"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":0.9937999844551086,"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/preconditioner","display_name":"Preconditioner","score":0.8840498924255371},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"Spectral radius","score":0.7373879551887512},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6659435033798218},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6369509696960449},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5753023624420166},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5711143016815186},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4916709065437317},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4891253113746643},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4443662762641907},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36319682002067566},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.24359974265098572},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17250850796699524},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07670065760612488}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8840498924255371},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.7373879551887512},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6659435033798218},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6369509696960449},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5753023624420166},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5711143016815186},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4916709065437317},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4891253113746643},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4443662762641907},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36319682002067566},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.24359974265098572},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17250850796699524},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07670065760612488},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2013/213659","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/213659","pdf_url":null,"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/1394807931","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394807931","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:doaj.org/article:4baa0dc8658946d4889a76362fb44ebb","is_oa":false,"landing_page_url":"https://doaj.org/article/4baa0dc8658946d4889a76362fb44ebb","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":null,"license_id":null,"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:10.1155/2013/213659","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/213659","pdf_url":null,"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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1980106372","https://openalex.org/W2083883802","https://openalex.org/W2168588855","https://openalex.org/W2619297956","https://openalex.org/W4295016751"],"related_works":["https://openalex.org/W4285325102","https://openalex.org/W1575783825","https://openalex.org/W2096346341","https://openalex.org/W2525981419","https://openalex.org/W3139004046","https://openalex.org/W2890462359","https://openalex.org/W3172804729","https://openalex.org/W4289542714","https://openalex.org/W2358739842","https://openalex.org/W4200609644"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2],"block":[3,7],"preconditioner":[4],"and":[5,23],"consider":[6],"preconditioned":[8],"SSOR":[9],"iterative":[10],"methods":[11,33,45],"for":[12,31],"solving":[13],"linear":[14],"system":[15],".":[16],"When":[17],"is":[18],"an":[19],"-matrix,":[20],"the":[21,28],"convergence":[22],"some":[24],"comparison":[25],"results":[26],"of":[27],"spectral":[29],"radius":[30],"our":[32,44],"are":[34,38,46],"given.":[35],"Numerical":[36],"examples":[37],"also":[39],"given":[40],"to":[41],"illustrate":[42],"that":[43],"valid.":[47]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
