{"id":"https://openalex.org/W1986408929","doi":"https://doi.org/10.1137/s0895479800376314","title":"New Band Toeplitz Preconditioners for Ill-Conditioned Symmetric Positive Definite Toeplitz Systems","display_name":"New Band Toeplitz Preconditioners for Ill-Conditioned Symmetric Positive Definite Toeplitz Systems","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1986408929","doi":"https://doi.org/10.1137/s0895479800376314","mag":"1986408929"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479800376314","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479800376314","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/A5008198354","display_name":"D. Noutsos","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. Noutsos","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078840132","display_name":"Paris Vassalos","orcid":"https://orcid.org/0000-0002-2131-7643"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. Vassalos","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3461,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.87581194,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"3","first_page":"728","last_page":"743"},"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":0.996999979019165,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.9440155029296875},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8354304432868958},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.7235531210899353},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.5641524195671082},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5374714732170105},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5123968720436096},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4837777316570282},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.46718505024909973},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.45063039660453796},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.4394929111003876},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.34480273723602295},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3358054757118225},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3261624574661255},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30855271220207214},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29654741287231445},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.14512741565704346}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.9440155029296875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8354304432868958},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.7235531210899353},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.5641524195671082},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5374714732170105},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5123968720436096},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4837777316570282},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.46718505024909973},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.45063039660453796},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.4394929111003876},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.34480273723602295},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3358054757118225},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3261624574661255},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30855271220207214},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29654741287231445},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.14512741565704346},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895479800376314","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479800376314","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.511.5955","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.511.5955","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uoi.gr/~dnoutsos/NV_SIMAX_2002.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1533471646","https://openalex.org/W1550150926","https://openalex.org/W1973255697","https://openalex.org/W1988177606","https://openalex.org/W1993856828","https://openalex.org/W1995772663","https://openalex.org/W2000583785","https://openalex.org/W2007407491","https://openalex.org/W2013541998","https://openalex.org/W2013737143","https://openalex.org/W2027035924","https://openalex.org/W2027175564","https://openalex.org/W2034472087","https://openalex.org/W2038166172","https://openalex.org/W2043909302","https://openalex.org/W2045463928","https://openalex.org/W2051015700","https://openalex.org/W2054781018","https://openalex.org/W2064616889","https://openalex.org/W2065451462","https://openalex.org/W2072820862","https://openalex.org/W2082691187","https://openalex.org/W2116496516","https://openalex.org/W2169487141","https://openalex.org/W2326028551","https://openalex.org/W3022136271","https://openalex.org/W4230445183","https://openalex.org/W4299000130","https://openalex.org/W4388534025"],"related_works":["https://openalex.org/W2361901126","https://openalex.org/W2349424752","https://openalex.org/W2070080181","https://openalex.org/W3160810049","https://openalex.org/W4237208466","https://openalex.org/W1482750774","https://openalex.org/W2986665254","https://openalex.org/W1994349276","https://openalex.org/W2015339619","https://openalex.org/W1826911152"],"abstract_inverted_index":{"It":[0],"is":[1,51,121,137],"well":[2],"known":[3],"that":[4,126,136,144],"preconditioned":[5,119],"conjugate":[6],"gradient":[7],"(PCG)":[8],"methods":[9],"are":[10],"widely":[11],"used":[12],"to":[13,69],"solve":[14],"ill-conditioned":[15],"Toeplitz":[16,36,105],"linear":[17],"systems":[18,37],"T":[19],"n":[20],"(f)x=b.":[21],"In":[22],"this":[23],"paper":[24],"we":[25,76],"present":[26],"a":[27,88,108,111,134,150],"new":[28],"preconditioning":[29],"technique":[30,129],"for":[31],"the":[32,54,60,65,96,102,115,127,156],"solution":[33],"of":[34,45,59,67,92,114,117],"symmetric":[35],"generated":[38],"by":[39,53,79,139],"nonnegative":[40],"functions":[41],"f":[42,50,68],"with":[43,63],"zeros":[44,64,66],"even":[46],"order.":[47],"More":[48],"specifically,":[49],"divided":[52],"appropriate":[55],"trigonometric":[56,82],"polynomial":[57],"g":[58],"smallest":[61],"degree,":[62],"eliminate":[70],"its":[71,118],"zeros.":[72],"Using":[73],"rational":[74],"approximation":[75,91],"approximate":[77],"$\\sqrt{f/g}$":[78],"$\\frac{p}{q}$,":[80],"$p,q$":[81],"polynomials":[83],"and":[84],"consider":[85],"$\\frac{p^2g}{q^2}$":[86],"as":[87,107],"very":[89,132],"satisfactory":[90],"f.":[93],"We":[94,123],"propose":[95],"matrix":[97,120],"$M_n=B^{-1}_n(q)B_n(p^2g)B^{-1}_n(q)$,":[98],"where":[99],"$B(\\cdot)$":[100],"denotes":[101],"associated":[103],"band":[104],"matrix,":[106],"preconditioner":[109],"whence":[110],"good":[112],"clustering":[113],"spectrum":[116],"obtained.":[122],"also":[124],"show":[125],"proposed":[128],"can":[130],"be":[131],"flexible,":[133],"fact":[135],"confirmed":[138],"various":[140],"numerical":[141],"experiments":[142],"so":[143],"in":[145],"many":[146],"cases":[147],"it":[148],"constitutes":[149],"much":[151],"more":[152],"efficient":[153],"strategy":[154],"than":[155],"existing":[157],"ones.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}