{"id":"https://openalex.org/W2002102128","doi":"https://doi.org/10.1137/s0895479801395458","title":"Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems","display_name":"Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2002102128","doi":"https://doi.org/10.1137/s0895479801395458","mag":"2002102128"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479801395458","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479801395458","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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":"last","author":{"id":"https://openalex.org/A5010561682","display_name":"Michael K. Ng","orcid":"https://orcid.org/0000-0001-6833-5227"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael K. Ng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.3761,"has_fulltext":false,"cited_by_count":1028,"citation_normalized_percentile":{"value":0.98959167,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"24","issue":"3","first_page":"603","last_page":"626"},"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":0.9993000030517578,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.8691020607948303},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.8396848440170288},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7712056636810303},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.6273465156555176},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5749551057815552},{"id":"https://openalex.org/keywords/arnoldi-iteration","display_name":"Arnoldi iteration","score":0.5508577227592468},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5192639827728271},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.51328444480896},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.4635652005672455},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4405745565891266},{"id":"https://openalex.org/keywords/hermitian-function","display_name":"Hermitian function","score":0.4383639395236969},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4192148447036743},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.3714596629142761},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.333279013633728},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1929912269115448},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13738369941711426},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09423801302909851}],"concepts":[{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.8691020607948303},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.8396848440170288},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7712056636810303},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.6273465156555176},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5749551057815552},{"id":"https://openalex.org/C43143463","wikidata":"https://www.wikidata.org/wiki/Q696822","display_name":"Arnoldi iteration","level":4,"score":0.5508577227592468},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5192639827728271},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.51328444480896},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.4635652005672455},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4405745565891266},{"id":"https://openalex.org/C146783285","wikidata":"https://www.wikidata.org/wiki/Q3236862","display_name":"Hermitian function","level":3,"score":0.4383639395236969},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4192148447036743},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.3714596629142761},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.333279013633728},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1929912269115448},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13738369941711426},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09423801302909851},{"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/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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479801395458","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479801395458","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1641159079","https://openalex.org/W1967647370","https://openalex.org/W1971116595","https://openalex.org/W1995582592","https://openalex.org/W2005041367","https://openalex.org/W2013336356","https://openalex.org/W2016901051","https://openalex.org/W2022480337","https://openalex.org/W2024670688","https://openalex.org/W2043875119","https://openalex.org/W2071705735","https://openalex.org/W2095036901","https://openalex.org/W2095483802","https://openalex.org/W2119862562","https://openalex.org/W2140153041","https://openalex.org/W2246376430","https://openalex.org/W2473084598","https://openalex.org/W4205624883"],"related_works":["https://openalex.org/W2015942935","https://openalex.org/W3134028852","https://openalex.org/W2037894849","https://openalex.org/W2804908571","https://openalex.org/W1971116595","https://openalex.org/W2561347830","https://openalex.org/W2169765983","https://openalex.org/W2034236710","https://openalex.org/W2058557317","https://openalex.org/W2148733093"],"abstract_inverted_index":{"We":[0],"study":[1],"efficient":[2],"iterative":[3],"methods":[4,28,50],"for":[5],"the":[6,18,24,39,60,68,74,78,90,94,102,105,112,115,124,146],"large":[7],"sparse":[8],"non-Hermitian":[9],"positive":[10],"definite":[11],"system":[12,79],"of":[13,23,59,77,80,89,93,104,111,114,126,137,148],"linear":[14,81],"equations":[15],"based":[16],"on":[17,101],"Hermitian":[19,106],"and":[20,35,108,129],"skew-Hermitian":[21],"splitting":[22,32,42],"coefficient":[25],"matrix.":[26],"These":[27],"include":[29],"a":[30,134,138],"Hermitian/skew-Hermitian":[31,41],"(HSS)":[33],"iteration":[34,54,96],"its":[36,52],"inexact":[37,40],"variant,":[38],"(IHSS)":[43],"iteration,":[44],"which":[45,97],"employs":[46],"some":[47],"Krylov":[48],"subspace":[49],"as":[51],"inner":[53],"processes":[55],"at":[56],"each":[57],"step":[58],"outer":[61],"HSS":[62,69,95,128],"iteration.":[63],"Theoretical":[64],"analyses":[65],"show":[66],"that":[67],"method":[70],"converges":[71],"unconditionally":[72],"to":[73,122,144],"unique":[75],"solution":[76],"equations.":[82],"Moreover,":[83],"we":[84],"derive":[85],"an":[86],"upper":[87],"bound":[88],"contraction":[91],"factor":[92],"is":[98,109,142],"dependent":[99],"solely":[100],"spectrum":[103],"part":[107],"independent":[110],"eigenvectors":[113],"matrices":[116],"involved.":[117],"Numerical":[118],"examples":[119],"are":[120],"presented":[121],"illustrate":[123,145],"effectiveness":[125],"both":[127],"IHSS":[130],"iterations.":[131],"In":[132],"addition,":[133],"model":[135],"problem":[136],"three-dimensional":[139],"convection-diffusion":[140],"equation":[141],"used":[143],"advantages":[147],"our":[149],"methods.":[150]},"counts_by_year":[{"year":2026,"cited_by_count":26},{"year":2025,"cited_by_count":41},{"year":2024,"cited_by_count":56},{"year":2023,"cited_by_count":50},{"year":2022,"cited_by_count":56},{"year":2021,"cited_by_count":65},{"year":2020,"cited_by_count":77},{"year":2019,"cited_by_count":63},{"year":2018,"cited_by_count":70},{"year":2017,"cited_by_count":65},{"year":2016,"cited_by_count":73},{"year":2015,"cited_by_count":79},{"year":2014,"cited_by_count":78},{"year":2013,"cited_by_count":50},{"year":2012,"cited_by_count":27}],"updated_date":"2026-06-18T10:00:31.954636","created_date":"2025-10-10T00:00:00"}