{"id":"https://openalex.org/W2016901051","doi":"https://doi.org/10.1137/0613059","title":"Acceleration of Relaxation Methods for Non-Hermitian Linear Systems","display_name":"Acceleration of Relaxation Methods for Non-Hermitian Linear Systems","publication_year":1992,"publication_date":"1992-07-01","ids":{"openalex":"https://openalex.org/W2016901051","doi":"https://doi.org/10.1137/0613059","mag":"2016901051"},"language":"en","primary_location":{"id":"doi:10.1137/0613059","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0613059","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/A5016985109","display_name":"Michael Eiermann","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"M. Eiermann","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053138852","display_name":"Wilhelm Niethammer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"W. Niethammer","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5058119240","display_name":"R. S. Varga","orcid":"https://orcid.org/0000-0003-1757-7140"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. S. Varga","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016985109"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4644,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.61204306,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"13","issue":"3","first_page":"979","last_page":"991"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9987000226974487,"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/T11809","display_name":"Advanced NMR Techniques and Applications","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.7889225482940674},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6900057196617126},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5916013717651367},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"Spectral radius","score":0.569762647151947},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.48936814069747925},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.4887533187866211},{"id":"https://openalex.org/keywords/hermitian-function","display_name":"Hermitian function","score":0.4351423680782318},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.41762447357177734},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4162021577358246},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34203028678894043},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33648306131362915},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2777807116508484},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2588430643081665},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2566078305244446},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.17227327823638916},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.12759166955947876}],"concepts":[{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.7889225482940674},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6900057196617126},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5916013717651367},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.569762647151947},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.48936814069747925},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.4887533187866211},{"id":"https://openalex.org/C146783285","wikidata":"https://www.wikidata.org/wiki/Q3236862","display_name":"Hermitian function","level":3,"score":0.4351423680782318},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.41762447357177734},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4162021577358246},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34203028678894043},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33648306131362915},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2777807116508484},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2588430643081665},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2566078305244446},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.17227327823638916},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.12759166955947876},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0613059","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0613059","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":12,"referenced_works":["https://openalex.org/W1969824614","https://openalex.org/W1972161707","https://openalex.org/W1978274896","https://openalex.org/W1992653386","https://openalex.org/W2011685366","https://openalex.org/W2019027232","https://openalex.org/W2019327644","https://openalex.org/W2023488486","https://openalex.org/W2073753111","https://openalex.org/W2082492903","https://openalex.org/W2569133694","https://openalex.org/W4214861729"],"related_works":["https://openalex.org/W2012515769","https://openalex.org/W2132739882","https://openalex.org/W2963690976","https://openalex.org/W1975001509","https://openalex.org/W2044453616","https://openalex.org/W4210393153","https://openalex.org/W3045365471","https://openalex.org/W4244117186","https://openalex.org/W4383621013","https://openalex.org/W3211576064"],"abstract_inverted_index":{"Let":[0],"$A":[1,64,95],"=":[2,11,26,65,73,96,104,189],"I":[3,105],"-":[4,67,98,109],"B":[5],"\\in":[6],"\\mathbb{C}^{n,n}":[7],"$,":[8,69],"with":[9,34,101,192],"diag$(B)":[10],"0$,":[12],"denote":[13],"a":[14,124,160,179,193,209,232,236],"nonsingular":[15],"non-Hermitian":[16],"matrix.":[17],"To":[18],"iteratively":[19],"solve":[20],"the":[21,81,120,143,151,155,169,183,186,206,226],"linear":[22],"system":[23],"$A{\\bf":[24],"x}":[25],"{\\bf":[27],"b}$,":[28],"two":[29,134],"splittings":[30],"of":[31,59,84,89,154,162,221],"A,":[32],"together":[33],"induced":[35],"relaxation":[36,121,125,145,171],"methods,":[37],"have":[38],"been":[39],"recently":[40],"investigated":[41],"in":[42,50,202],"[W.":[43],"Niethammer":[44],"and":[45],"R.":[46],"S.":[47],"Varga,":[48],"Results":[49],"Math.,":[51],"16":[52],"(1989),":[53],"pp.":[54],"308\u2013320].":[55],"The":[56,86,136],"Hermitian":[57,82,184],"splitting":[58,88],"A":[60,75,90,108],"is":[61,80,91,139,165,212,215,239],"defined":[62,93],"by":[63,94,132,178],"M^h":[66],"N^h":[68],"where":[70],"$M^h":[71],":":[72,103],"(":[74,107],"+":[76,106],"A^":[77,110],"*":[78],")/2$":[79],"part":[83],"A.":[85],"skew-Hermitian":[87,207],"similarly":[92],"M^s":[97],"N^s":[99],"$":[100,148,164],"$M^s":[102],"*)/2$.":[111],"This":[112],"paper":[113],"considers":[114],"k-step":[115,180],"iterative":[116],"methods":[117],"to":[118,141,199],"accelerate":[119],"schemes":[122],"(involving":[123],"factor":[126,146],"$\\omega":[127,147,163,188],"$)":[128],"that":[129,149,168,214],"are":[130],"generated":[131],"these":[133],"splittings.":[135],"primary":[137],"interest":[138],"not":[140],"determine":[142],"optimal":[144,201],"minimizes":[150],"spectral":[152],"radius":[153],"associated":[156],"iteration":[157],"operator.":[158],"Rather,":[159],"value":[161],"sought":[166],"such":[167],"resulting":[170],"method":[172,229],"can":[173],"be":[174,200],"most":[175],"efficiently":[176],"accelerated":[177],"method.":[181],"For":[182,205],"splitting,":[185,208],"choice":[187],"1$":[190],"(together":[191],"suitable":[194],"Chebyshev":[195],"acceleration)":[196],"turns":[197],"out":[198],"this":[203,222],"sense.":[204],"hybrid":[210,224],"scheme":[211],"proposed":[213],"nearly":[216],"optimal.":[217],"As":[218],"another":[219],"application":[220],"latter":[223],"procedure,":[225],"block":[227],"Jacobi":[228],"arising":[230],"from":[231],"model":[233],"equation":[234],"for":[235],"convection-diffusion":[237],"problem":[238],"analyzed.":[240]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}