{"id":"https://openalex.org/W1993509058","doi":"https://doi.org/10.1137/s0895479803422701","title":"A Stability Property of T. Chan's Preconditioner","display_name":"A Stability Property of T. Chan's Preconditioner","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1993509058","doi":"https://doi.org/10.1137/s0895479803422701","mag":"1993509058"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479803422701","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479803422701","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/A5005037066","display_name":"Xiaoqing Jin","orcid":"https://orcid.org/0000-0002-8836-3505"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xiao-Qing Jin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014988509","display_name":"Yimin Wei","orcid":"https://orcid.org/0000-0001-6192-0546"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yi-Min Wei","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101604233","display_name":"Wei Xu","orcid":"https://orcid.org/0000-0003-1807-2996"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wei XU","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005037066"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7091,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.69063901,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":"3","first_page":"627","last_page":"629"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9832000136375427,"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":0.9822999835014343,"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/circulant-matrix","display_name":"Circulant matrix","score":0.8425850868225098},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.8349343538284302},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.8266699910163879},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6958668828010559},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.5397542119026184},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5362756848335266},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5047053098678589},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41951581835746765},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.35979723930358887},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2749332785606384},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13925206661224365},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12177282571792603},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.06027412414550781}],"concepts":[{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.8425850868225098},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.8349343538284302},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8266699910163879},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6958668828010559},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.5397542119026184},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5362756848335266},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5047053098678589},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41951581835746765},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.35979723930358887},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2749332785606384},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13925206661224365},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12177282571792603},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.06027412414550781},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479803422701","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479803422701","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W605044866","https://openalex.org/W852592595","https://openalex.org/W1533471646","https://openalex.org/W2005041367","https://openalex.org/W2027778162","https://openalex.org/W2080097309","https://openalex.org/W2092085096"],"related_works":["https://openalex.org/W3177828492","https://openalex.org/W2034415022","https://openalex.org/W2335757200","https://openalex.org/W2149698301","https://openalex.org/W4388372565","https://openalex.org/W63525287","https://openalex.org/W2286689764","https://openalex.org/W2026406497","https://openalex.org/W4388372654","https://openalex.org/W2674186696"],"abstract_inverted_index":{"Previous":[0,257],"article":[1,3,258,260],"Next":[2,259],"A":[4,141,233,296,314,348],"Stability":[5,225],"Property":[6],"of":[7,75,188,319,336],"T.":[8,35,298,320,337,351],"Chan's":[9,36,254,387],"PreconditionerXiao-Qing":[10],"Jin,":[11,17,184],"Yi-Min":[12,18],"Wei,":[13,19],"and":[14,20,57,64,89,145,154,186,194,217,226,268,316,324,341,355,371,384,404],"Wei":[15,21],"XUXiao-Qing":[16],"XUhttps://doi.org/10.1137/S0895479803422701PDFBibTexSections":[22],"ToolsAdd":[23],"to":[24],"favoritesExport":[25],"CitationTrack":[26],"CitationsEmail":[27],"SectionsAboutAbstractIn":[28],"this":[29],"short":[30],"note,":[31],"we":[32],"prove":[33],"that":[34,54],"preconditioner":[37,113,300],"proposed":[38],"in":[39,71,172,214],"{TChan}":[40],"[SIAM":[41],"J.":[42,118,163],"Sci.":[43,119],"Statist.":[44,120],"Comput.,":[45,121],"9":[46,122],"(1988),":[47,123],"pp.":[48,244],"766--771]":[49],"is":[50],"stable":[51],"for":[52,96,114,157,235,282,301,382,402],"matrices":[53,156],"are":[55],"normal":[56],"stable.[1]":[58],"Raymond":[59,87],"Chan,":[60,109],",":[61,65,90],"Xiao\u2010Qing":[62,183],"Jin":[63],"Man\u2010Chung":[66],"Yeung,":[67],"The":[68,263],"circulant":[69,112,255,280,388],"operator":[70],"the":[72],"Banach":[73],"algebra":[74,175],"matrices,":[76,133],"Linear":[77],"Algebra":[78,267,323,340,354],"Appl.,":[79,166],"149":[80],"(1991),":[81],"41\u201353":[82],"10.1016/0024-3795(91)90324-P":[83],"92f:15004":[84],"CrossrefISIGoogle":[85,252],"Scholar[2]":[86],"Chan":[88],"Michael":[91],"Ng,":[92],"Conjugate":[93],"gradient":[94],"methods":[95,171],"Toeplitz":[97,115,159,190,236,302],"systems,":[98,116,211],"SIAM":[99,117,162],"Rev.,":[100],"38":[101],"(1996),":[102],"427\u2013482":[103],"10.1137/S0036144594276474":[104],"97i:65048":[105],"LinkISIGoogle":[106,126,181],"Scholar[3]":[107],"Tony":[108],"An":[110],"optimal":[111],"766\u2013771":[124],"89e:65046":[125],"Scholar[4]":[127],"Google":[128,149,205,229],"Scholar[5]":[129],"Philip":[130],"Davis,":[131],"Circulant":[132,153],"John":[134],"Wiley":[135],"&":[136,286,304,393],"Sons,":[137],"New":[138],"York\u2010Chichester\u2010Brisbane,":[139],"1979xv+250,":[140],"Wiley\u2010Interscience":[142],"Publication;":[143],"Pure":[144],"Applied":[146,385,405],"Mathematics":[147,287,305,406],"81a:15003":[148],"Scholar[6]":[150],"Thomas":[151],"Huckle,":[152],"skewcirculant":[155],"solving":[158],"matrix":[160,237],"problems,":[161],"Matrix":[164,369],"Anal.":[165],"13":[167],"(1992),":[168],"767\u2013777,":[169],"Iterative":[170],"numerical":[173],"linear":[174,284],"(Copper":[176],"Mountain,":[177],"CO,":[178],"1990)":[179],"93e:65073":[180],"Scholar[7]":[182],"Developments":[185],"applications":[187],"block":[189],"iterative":[191],"solvers,":[192],"Combinatorics":[193],"Computer":[195],"Science,":[196],"Vol.":[197,219,271,290,308,327,344,358],"2,":[198],"Kluwer":[199],"Academic":[200],"Publishers":[201],"Group,":[202],"2002xiv+218":[203],"1980639":[204],"Scholar[8]":[206],"Dragoslav":[207],"\u0160iljak,":[208],"Large\u2010scale":[209],"dynamic":[210],"North\u2010Holland":[212,221],"Series":[213],"System":[215],"Science":[216],"Engineering,":[218],"3,":[220],"Publishing":[222],"Co.,":[223],"1979xvi+416,":[224],"structure":[227],"82j:93004":[228],"Scholar[9]":[230],"G.":[231],"Strang,":[232],"proposal":[234],"calculations,":[238],"Stud.":[239,249],"Appl.":[240,250],"Math.,":[241],"74":[242],"(1986),":[243],"171\u2013176.":[245],"std":[246],"SAPMB6":[247],"0022-2526":[248],"Math.":[251],"ScholarKeywordsT.":[253],"preconditionerstable":[256],"FiguresRelatedReferencesCited":[261],"byDetails":[262],"generalized":[264],"superoptimal":[265],"preconditionerLinear":[266,322,339,353],"its":[269,325,342,356],"Applications,":[270,289,307,326,343,357],"432,":[272],"No.":[273,292,310,329],"1":[274],"Cross":[275,294,312,331,346,360],"Ref":[276,295,313,332,347,361],"Block":[277],"preconditioners":[278],"with":[279,288,306],"blocks":[281],"general":[283],"systemsComputers":[285,303],"58,":[291,309],"7":[293],"modified":[297],"Chan\u2019s":[299,321,338,352],"4":[311],"survey":[315],"some":[317],"extensions":[318],"428,":[328],"2-3":[330],"Some":[333],"stability":[334],"properties":[335],"395":[345],"note":[349],"on":[350,368],"376":[359],"Volume":[362],"25,":[363],"Issue":[364],"3|":[365],"2003SIAM":[366],"Journal":[367],"Analysis":[370],"Applications":[372],"History":[373],"Published":[374],"online:31":[375],"July":[376],"2006":[377],"InformationCopyright":[378],"\u00a9":[379],"2003":[380],"Society":[381],"Industrial":[383,403],"MathematicsKeywordsT.":[386],"preconditionerstableMSC":[389],"codes65F1065N2265L0565F15PDF":[390],"Download":[391],"Article":[392],"Publication":[394],"DataArticle":[395],"DOI:10.1137/S0895479803422701Article":[396],"page":[397],"range:pp.":[398],"627-629ISSN":[399],"(print):0895-4798ISSN":[400],"(online):1095-7162Publisher:Society":[401]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}