{"id":"https://openalex.org/W2088456940","doi":"https://doi.org/10.1137/s1064827503428114","title":"Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems","display_name":"Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2088456940","doi":"https://doi.org/10.1137/s1064827503428114","mag":"2088456940"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827503428114","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827503428114","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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/A5113970855","display_name":"Zhong\u2010Zhi Bai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhong-Zhi Bai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110003399","display_name":"Gene H. Golub","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gene H. Golub","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056471810","display_name":"Linzhang Lu","orcid":"https://orcid.org/0000-0003-1330-7020"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin-Zhang Lu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108133091","display_name":"Jun-Feng Yin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jun-Feng Yin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.4213,"has_fulltext":false,"cited_by_count":317,"citation_normalized_percentile":{"value":0.98044022,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"26","issue":"3","first_page":"844","last_page":"863"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9976999759674072,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9955000281333923,"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":0.822320818901062},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.785552978515625},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7745836973190308},{"id":"https://openalex.org/keywords/triangular-matrix","display_name":"Triangular matrix","score":0.6711020469665527},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6274756193161011},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5445625185966492},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5120392441749573},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5025167465209961},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.49164658784866333},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.4290030002593994},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.41680753231048584},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36534547805786133},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32089072465896606},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.30047672986984253},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21624049544334412},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08862122893333435},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07917410135269165}],"concepts":[{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.822320818901062},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.785552978515625},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7745836973190308},{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.6711020469665527},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6274756193161011},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5445625185966492},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5120392441749573},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5025167465209961},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.49164658784866333},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.4290030002593994},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41680753231048584},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36534547805786133},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32089072465896606},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30047672986984253},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21624049544334412},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08862122893333435},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07917410135269165},{"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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1064827503428114","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827503428114","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.5.1823","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.5.1823","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-sccm.stanford.edu/pub/sccm/sccm03-09.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W2002102128","https://openalex.org/W2025437891","https://openalex.org/W2043857934","https://openalex.org/W2049726926","https://openalex.org/W2073753111","https://openalex.org/W2140153041","https://openalex.org/W2144982983","https://openalex.org/W3035235874"],"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/W2951116071","https://openalex.org/W2371640884","https://openalex.org/W1984769443","https://openalex.org/W3156339903","https://openalex.org/W2016499627"],"abstract_inverted_index":{"By":[0],"further":[1],"generalizing":[2],"the":[3,43,57,68],"concept":[4],"of":[5,34,61],"Hermitian":[6,44],"(or":[7,45],"normal)":[8,46],"and":[9,15,25,29,36,47],"skew-Hermitian":[10,26,37,48],"splitting":[11,38,49],"for":[12,54],"a":[13,20,32],"non-Hermitian":[14],"positive-definite":[16,24],"matrix,":[17],"we":[18],"introduce":[19],"new":[21],"splitting,":[22,28],"called":[23],"(PS)":[27],"then":[30],"establish":[31],"class":[33],"positivedefinite":[35],"(PSS)":[39],"methods":[40],"similar":[41],"to":[42],"(HSS":[50],"or":[51],"NSS)":[52],"method":[53,70],"iteratively":[55],"solving":[56],"positive":[58],"definite":[59],"systems":[60],"linear":[62],"equations.":[63],"Theoretical":[64],"analysis":[65],"shows":[66],"that":[67],"PSS":[69],"converges":[71],"#":[72],"Subsidized":[73],"by":[74],"The":[75],"Special":[76],"Funds":[77],"For":[78],"Major":[79],"State":[80],"Basic":[81],"Research":[82],"Projects":[83],"G1999032803.":[84]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":16},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":26},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":20},{"year":2017,"cited_by_count":31},{"year":2016,"cited_by_count":31},{"year":2015,"cited_by_count":27},{"year":2014,"cited_by_count":30},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":11}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}