{"id":"https://openalex.org/W2009646459","doi":"https://doi.org/10.1155/2014/628069","title":"More on Generalizations and Modifications of Iterative Methods for Solving Large Sparse Indefinite Linear Systems","display_name":"More on Generalizations and Modifications of Iterative Methods for Solving Large Sparse Indefinite Linear Systems","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2009646459","doi":"https://doi.org/10.1155/2014/628069","mag":"2009646459"},"language":"en","primary_location":{"id":"doi:10.1155/2014/628069","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/628069","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/628069.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/2014/628069.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006434046","display_name":"Jen-Yuan Chen","orcid":"https://orcid.org/0000-0002-7932-7430"},"institutions":[{"id":"https://openalex.org/I135551196","display_name":"National Kaohsiung Normal University","ror":"https://ror.org/04tsc8g87","country_code":"TW","type":"education","lineage":["https://openalex.org/I135551196"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Jen-Yuan Chen","raw_affiliation_strings":["Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 81201, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-7932-7430","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 81201, Taiwan","institution_ids":["https://openalex.org/I135551196"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061271218","display_name":"David R. Kincaid","orcid":null},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David R. Kincaid","raw_affiliation_strings":["Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009836266","display_name":"Yu-Chien Li","orcid":null},"institutions":[{"id":"https://openalex.org/I135551196","display_name":"National Kaohsiung Normal University","ror":"https://ror.org/04tsc8g87","country_code":"TW","type":"education","lineage":["https://openalex.org/I135551196"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yu-Chien Li","raw_affiliation_strings":["Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 81201, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 81201, Taiwan","institution_ids":["https://openalex.org/I135551196"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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":0,"citation_normalized_percentile":{"value":0.08359533,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"15"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9972000122070312,"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/variety","display_name":"Variety (cybernetics)","score":0.6371921300888062},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.603058934211731},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5968561172485352},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.59581458568573},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5655606985092163},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.5390431880950928},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2985526919364929},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10410037636756897},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08447375893592834}],"concepts":[{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.6371921300888062},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.603058934211731},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5968561172485352},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.59581458568573},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5655606985092163},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.5390431880950928},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2985526919364929},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10410037636756897},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08447375893592834}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2014/628069","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/628069","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/628069.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/1425050614","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1425050614","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:628069","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/628069.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:0b6c08d730bf481e935fecbe65e7b249","is_oa":true,"landing_page_url":"https://doaj.org/article/0b6c08d730bf481e935fecbe65e7b249","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 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/628069","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/628069","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/628069.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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2009646459.pdf","grobid_xml":"https://content.openalex.org/works/W2009646459.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1502825029","https://openalex.org/W1506342804","https://openalex.org/W2018850201","https://openalex.org/W2076437358","https://openalex.org/W2117686912","https://openalex.org/W2140153041","https://openalex.org/W2798909945"],"related_works":["https://openalex.org/W2032899988","https://openalex.org/W2072568196","https://openalex.org/W2971922054","https://openalex.org/W2610002741","https://openalex.org/W4220970845","https://openalex.org/W1579526657","https://openalex.org/W2066215857","https://openalex.org/W4226335490","https://openalex.org/W3146700705","https://openalex.org/W2552362573"],"abstract_inverted_index":{"Continuing":[0],"from":[1],"the":[2],"works":[3],"of":[4,22,34,41],"Li":[5,9],"et":[6,13],"al.":[7,14],"(2014),":[8],"(2007),":[10],"and":[11,20,30,54],"Kincaid":[12],"(2000),":[15],"we":[16],"present":[17],"more":[18],"generalizations":[19],"modifications":[21],"iterative":[23,42],"methods":[24,43],"for":[25],"solving":[26],"large":[27],"sparse":[28],"symmetric":[29],"nonsymmetric":[31],"indefinite":[32],"systems":[33],"linear":[35],"equations.":[36],"We":[37],"discuss":[38],"a":[39],"variety":[40],"such":[44],"as":[45],"GMRES,":[46],"MGMRES,":[47],"MINRES,":[48,51],"LQ-MINRES,":[49],"QR":[50],"MMINRES,":[52],"MGRES,":[53],"others.":[55]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}