{"id":"https://openalex.org/W2165741100","doi":"https://doi.org/10.1090/s0025-5718-06-01892-8","title":"Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices","display_name":"Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices","publication_year":2006,"publication_date":"2006-08-31","ids":{"openalex":"https://openalex.org/W2165741100","doi":"https://doi.org/10.1090/s0025-5718-06-01892-8","mag":"2165741100"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-06-01892-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01892-8","pdf_url":"https://www.ams.org/mcom/2007-76-257/S0025-5718-06-01892-8/S0025-5718-06-01892-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2007-76-257/S0025-5718-06-01892-8/S0025-5718-06-01892-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113970855","display_name":"Zhong\u2010Zhi Bai","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhong-Zhi Bai","raw_affiliation_strings":["Department of Mathematics, Fudan University, Shanghai 200433, People\u00e2\u0080\u0099s Republic of China, and State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, People\u00e2\u0080\u0099s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Fudan University, Shanghai 200433, People\u00e2\u0080\u0099s Republic of China, and State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366","https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110003399","display_name":"Gene H. Golub","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gene Golub","raw_affiliation_strings":["Scientific Computing and Computational Mathematics Program, Department of Computer Science, Stanford University, Stanford, California 94305-9025"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Scientific Computing and Computational Mathematics Program, Department of Computer Science, Stanford University, Stanford, California 94305-9025","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102931711","display_name":"Chi-Kwong Li","orcid":"https://orcid.org/0000-0002-4825-6270"},"institutions":[{"id":"https://openalex.org/I16285277","display_name":"William & Mary","ror":"https://ror.org/03hsf0573","country_code":"US","type":"education","lineage":["https://openalex.org/I16285277"]},{"id":"https://openalex.org/I267592682","display_name":"Williams (United States)","ror":"https://ror.org/007zhvp17","country_code":"US","type":"company","lineage":["https://openalex.org/I267592682"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chi-Kwong Li","raw_affiliation_strings":["Department of Mathematics, The College of William & Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The College of William & Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795","institution_ids":["https://openalex.org/I16285277","https://openalex.org/I267592682"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0474,"has_fulltext":true,"cited_by_count":181,"citation_normalized_percentile":{"value":0.9415507,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":100},"biblio":{"volume":"76","issue":"257","first_page":"287","last_page":"298"},"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":0.9976999759674072,"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":0.9951000213623047,"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/hermitian-matrix","display_name":"Hermitian matrix","score":0.8852109909057617},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7955383658409119},{"id":"https://openalex.org/keywords/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.649587094783783},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6292136311531067},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.570906400680542},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5314354300498962},{"id":"https://openalex.org/keywords/hermitian-function","display_name":"Hermitian function","score":0.5107010006904602},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24691054224967957},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1781652569770813},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07765674591064453}],"concepts":[{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.8852109909057617},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7955383658409119},{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.649587094783783},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6292136311531067},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.570906400680542},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5314354300498962},{"id":"https://openalex.org/C146783285","wikidata":"https://www.wikidata.org/wiki/Q3236862","display_name":"Hermitian function","level":3,"score":0.5107010006904602},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24691054224967957},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1781652569770813},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07765674591064453},{"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/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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-06-01892-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01892-8","pdf_url":"https://www.ams.org/mcom/2007-76-257/S0025-5718-06-01892-8/S0025-5718-06-01892-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.153.6512","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.6512","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2007-76-257/S0025-5718-06-01892-8/S0025-5718-06-01892-8.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.78.1952","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.78.1952","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.resnet.wm.edu/~cklixx/baili2nd.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-06-01892-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01892-8","pdf_url":"https://www.ams.org/mcom/2007-76-257/S0025-5718-06-01892-8/S0025-5718-06-01892-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4699999988079071,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G2291801174","display_name":"\u7ebf\u6027\u978d\u70b9\u95ee\u9898\u7684\u9ad8\u6027\u80fd\u7b97\u6cd5\u4e0e\u6536\u655b\u7406\u8bba","funder_award_id":"10471146","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2328675308","display_name":null,"funder_award_id":"2005CB321702","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3712234867","display_name":null,"funder_award_id":"2005CB321702","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5541320598","display_name":null,"funder_award_id":"2005CB321702","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G7972242949","display_name":"ADVANCED COMPUTING FOR 21ST   CENTURY ACCELERATOR SCIENCE   AND TECHNOLOGY","funder_award_id":"FC02-01ER41177","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321851","display_name":"Fudan University","ror":"https://ror.org/013q1eq08"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2165741100.pdf","grobid_xml":"https://content.openalex.org/works/W2165741100.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W1524324710","https://openalex.org/W1586776267","https://openalex.org/W1606462009","https://openalex.org/W1641159079","https://openalex.org/W1852082788","https://openalex.org/W1963751327","https://openalex.org/W1967647370","https://openalex.org/W1970870428","https://openalex.org/W1974512823","https://openalex.org/W1980281413","https://openalex.org/W1981745143","https://openalex.org/W1991285463","https://openalex.org/W1995582592","https://openalex.org/W2002102128","https://openalex.org/W2009334761","https://openalex.org/W2025529701","https://openalex.org/W2029367872","https://openalex.org/W2040807801","https://openalex.org/W2048752392","https://openalex.org/W2049726926","https://openalex.org/W2050206349","https://openalex.org/W2063717873","https://openalex.org/W2067325378","https://openalex.org/W2068395392","https://openalex.org/W2069601896","https://openalex.org/W2089141442","https://openalex.org/W2092439735","https://openalex.org/W2129625121","https://openalex.org/W2168690621","https://openalex.org/W2177784766","https://openalex.org/W2798909945","https://openalex.org/W3149667697"],"related_works":["https://openalex.org/W2367027423","https://openalex.org/W2009320932","https://openalex.org/W4206234077","https://openalex.org/W1993806324","https://openalex.org/W2121030460","https://openalex.org/W3137086316","https://openalex.org/W2951116071","https://openalex.org/W2371640884","https://openalex.org/W1992775510","https://openalex.org/W3156339903"],"abstract_inverted_index":{"For":[0],"the":[1,18,22,47,52],"non-Hermitian":[2],"and":[3,13,25,55],"positive":[4],"semidefinite":[5],"systems":[6,39],"of":[7,21,51],"linear":[8,38],"equations,":[9],"we":[10],"derive":[11],"necessary":[12],"sufficient":[14],"conditions":[15,45],"for":[16,46],"guaranteeing":[17],"unconditional":[19],"convergence":[20,44],"preconditioned":[23,53],"Hermitian":[24,54],"skew-Hermitian":[26,56],"splitting":[27,57],"iteration":[28,58],"methods.":[29,59],"We":[30],"then":[31],"apply":[32],"these":[33],"results":[34],"to":[35,42],"block":[36,49],"tridiagonal":[37],"in":[40],"order":[41],"obtain":[43],"corresponding":[48],"variants":[50]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":21},{"year":2016,"cited_by_count":18},{"year":2015,"cited_by_count":23},{"year":2014,"cited_by_count":21},{"year":2013,"cited_by_count":16},{"year":2012,"cited_by_count":10}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}