{"id":"https://openalex.org/W2084730628","doi":"https://doi.org/10.1137/s0036142999354083","title":"The Best Circulant Preconditioners for Hermitian Toeplitz Systems","display_name":"The Best Circulant Preconditioners for Hermitian Toeplitz Systems","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2084730628","doi":"https://doi.org/10.1137/s0036142999354083","mag":"2084730628"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142999354083","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999354083","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5004126693","display_name":"Raymond H. Chan","orcid":"https://orcid.org/0000-0003-0910-4685"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Raymond H. Chan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000385200","display_name":"Andy M. Yip","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andy M. Yip","raw_affiliation_strings":[],"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":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5004126693"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.1793,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.91975405,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"38","issue":"3","first_page":"876","last_page":"896"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9973000288009644,"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/T10849","display_name":"Finite Group Theory Research","score":0.9884999990463257,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/circulant-matrix","display_name":"Circulant matrix","score":0.8749352693557739},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.8725792169570923},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8561922311782837},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.7911463379859924},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.7288141250610352},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.6905503273010254},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6042647957801819},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.583256185054779},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5565982460975647},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.518059492111206},{"id":"https://openalex.org/keywords/uniform-boundedness","display_name":"Uniform boundedness","score":0.49641066789627075},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.469390332698822},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45227155089378357},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4117390215396881},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3858742415904999},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2946512699127197},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2915210723876953},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17963102459907532}],"concepts":[{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.8749352693557739},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.8725792169570923},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8561922311782837},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.7911463379859924},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.7288141250610352},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.6905503273010254},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6042647957801819},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.583256185054779},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5565982460975647},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.518059492111206},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.49641066789627075},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.469390332698822},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45227155089378357},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4117390215396881},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3858742415904999},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2946512699127197},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2915210723876953},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17963102459907532},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142999354083","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999354083","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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":26,"referenced_works":["https://openalex.org/W114314968","https://openalex.org/W1493981498","https://openalex.org/W1504178724","https://openalex.org/W1533471646","https://openalex.org/W1554635237","https://openalex.org/W1965720095","https://openalex.org/W1973255697","https://openalex.org/W1974535680","https://openalex.org/W1988177606","https://openalex.org/W1991469062","https://openalex.org/W1994176509","https://openalex.org/W1997992827","https://openalex.org/W2005041367","https://openalex.org/W2010384703","https://openalex.org/W2026406497","https://openalex.org/W2045682702","https://openalex.org/W2055507002","https://openalex.org/W2080097309","https://openalex.org/W2082509218","https://openalex.org/W2095018839","https://openalex.org/W2162176806","https://openalex.org/W2169487141","https://openalex.org/W2609065776","https://openalex.org/W2610857016","https://openalex.org/W4238784554","https://openalex.org/W4239165712"],"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/W2793283006","https://openalex.org/W2011798910"],"abstract_inverted_index":{"In":[0,149],"this":[1],"paper,":[2],"we":[3,156],"propose":[4],"a":[5,65,70],"new":[6,173],"family":[7],"of":[8,29,44,51,60,72,98,138,144,171],"circulant":[9,174],"preconditioners":[10,20,46],"for":[11,106],"ill-conditioned":[12],"Hermitian":[13],"Toeplitz":[14,39],"systems":[15],"Ax":[16],"=":[17],"b.":[18],"The":[19,135],"are":[21,165],"constructed":[22],"by":[23],"convolving":[24],"the":[25,32,42,45,49,57,75,96,99,112,122,130,140,150,159,169],"generating":[26],"function":[27,68],"f":[28,63,153],"A":[30,52,78],"with":[31,69],"generalized":[33],"Jackson":[34],"kernels.":[35],"For":[36],"an":[37],"n-by-n":[38],"matrix":[40,101],"A,":[41],"construction":[43],"requires":[47],"only":[48],"entries":[50],"and":[53,95],"does":[54],"not":[55],"require":[56],"explicit":[58],"knowledge":[59],"f.":[61],"When":[62],"is":[64,79,92,102,115,142,154,161],"nonnegative":[66],"continuous":[67],"zero":[71],"order":[73],"2p,":[74],"condition":[76],"numberof":[77],"known":[80],"to":[81,128,167],"grow":[82],"as":[83],"O(n2p":[84],").":[85],"We":[86],"show,":[87],"however,":[88],"that":[89,158],"our":[90,172],"preconditioner":[91],"positive":[93],"definite":[94],"spectrum":[97],"preconditioned":[100,131],"uniformly":[103,116],"bounded":[104,117],"except":[105],"at":[107],"most":[108],"2p+1":[109],"outliers.":[110],"Moreover,":[111],"smallest":[113],"eigenvalue":[114],"away":[118],"from":[119],"zero.":[120],"Hence":[121],"conjugate":[123],"gradient":[124],"method,":[125],"when":[126,152],"applied":[127],"solving":[129,139],"system,":[132],"converges":[133],"linearly.":[134],"total":[136],"complexity":[137],"system":[141],"therefore":[143],"O(n":[145],"log":[146],"n)":[147],"operations.":[148],"case":[151],"positive,":[155],"show":[157],"convergence":[160],"superlinear.":[162],"Numerical":[163],"results":[164],"included":[166],"illustrate":[168],"effectiveness":[170],"preconditioners.":[175]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}