{"id":"https://openalex.org/W2004529037","doi":"https://doi.org/10.1137/s0895479803428230","title":"Block Diagonal and Schur Complement Preconditioners for Block-Toeplitz Systems with Small Size Blocks","display_name":"Block Diagonal and Schur Complement Preconditioners for Block-Toeplitz Systems with Small Size Blocks","publication_year":2007,"publication_date":"2007-11-10","ids":{"openalex":"https://openalex.org/W2004529037","doi":"https://doi.org/10.1137/s0895479803428230","mag":"2004529037"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479803428230","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479803428230","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/A5086061723","display_name":"Wai\u2010Ki Ching","orcid":"https://orcid.org/0000-0002-5785-3210"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Wai-Ki Ching","raw_affiliation_strings":["The University of Hong Kong"],"affiliations":[{"raw_affiliation_string":"The University of Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010561682","display_name":"Michael K. Ng","orcid":"https://orcid.org/0000-0001-6833-5227"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Michael K. Ng","raw_affiliation_strings":["Department of Mathematics"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics","institution_ids":["https://openalex.org/I530967"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033802995","display_name":"You\u2010Wei Wen","orcid":"https://orcid.org/0000-0002-9892-3668"},"institutions":[{"id":"https://openalex.org/I101479585","display_name":"South China Agricultural University","ror":"https://ror.org/05v9jqt67","country_code":"CN","type":"education","lineage":["https://openalex.org/I101479585"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"You-Wei Wen","raw_affiliation_strings":["South China agricultural university"],"affiliations":[{"raw_affiliation_string":"South China agricultural university","institution_ids":["https://openalex.org/I101479585"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5086061723"],"corresponding_institution_ids":["https://openalex.org/I889458895"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.09331728,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"29","issue":"4","first_page":"1101","last_page":"1119"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9994999766349792,"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":0.9994999766349792,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9847999811172485,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9821000099182129,"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/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.8738390207290649},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8047401309013367},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.7855313420295715},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.6807237863540649},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.6151391267776489},{"id":"https://openalex.org/keywords/levinson-recursion","display_name":"Levinson recursion","score":0.4962611794471741},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.4539952874183655},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4042561650276184},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.19592440128326416},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.13922864198684692}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.8738390207290649},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8047401309013367},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.7855313420295715},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.6807237863540649},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6151391267776489},{"id":"https://openalex.org/C122212055","wikidata":"https://www.wikidata.org/wiki/Q11679774","display_name":"Levinson recursion","level":3,"score":0.4962611794471741},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.4539952874183655},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4042561650276184},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.19592440128326416},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.13922864198684692},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0895479803428230","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479803428230","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:10.1.1.568.9313","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.568.9313","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hkumath.hku.hk/~imr/IMRPreprintSeries/2006/IMR2006-12.pdf","raw_type":"text"},{"id":"pmh:oai:hub.hku.hk:10722/75407","is_oa":false,"landing_page_url":"http://hdl.handle.net/10722/75407","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W32891743","https://openalex.org/W45545812","https://openalex.org/W124312991","https://openalex.org/W323572456","https://openalex.org/W1492221128","https://openalex.org/W1504797307","https://openalex.org/W1533471646","https://openalex.org/W1546004968","https://openalex.org/W1587896874","https://openalex.org/W1627054999","https://openalex.org/W1964097419","https://openalex.org/W1970334228","https://openalex.org/W1973255697","https://openalex.org/W1975696503","https://openalex.org/W1988976163","https://openalex.org/W1991469062","https://openalex.org/W2003977554","https://openalex.org/W2005041367","https://openalex.org/W2011798910","https://openalex.org/W2014835357","https://openalex.org/W2020391398","https://openalex.org/W2020914406","https://openalex.org/W2024597248","https://openalex.org/W2034472087","https://openalex.org/W2036555840","https://openalex.org/W2040633589","https://openalex.org/W2041103874","https://openalex.org/W2054781018","https://openalex.org/W2058478885","https://openalex.org/W2080097309","https://openalex.org/W2084730628","https://openalex.org/W2086517326","https://openalex.org/W2092085096","https://openalex.org/W2094067340","https://openalex.org/W2095018839","https://openalex.org/W2162176806","https://openalex.org/W2163899311","https://openalex.org/W2169487141","https://openalex.org/W2610857016"],"related_works":["https://openalex.org/W2081990255","https://openalex.org/W110533479","https://openalex.org/W1981369412","https://openalex.org/W4248194227","https://openalex.org/W2088576025","https://openalex.org/W2158178606","https://openalex.org/W2047814828","https://openalex.org/W1998860845","https://openalex.org/W2059885882","https://openalex.org/W2004529037"],"abstract_inverted_index":{"In":[0],"this":[1,55],"paper":[2],"we":[3],"consider":[4],"the":[5,38,41,61,64,100,105,132,135],"solution":[6],"of":[7,40,52,63,88,104,107,134],"Hermitian":[8],"positive":[9],"definite":[10],"block-Toeplitz":[11,29,36,77,109,113],"systems":[12,78,114],"with":[13,79],"small":[14,80],"size":[15,62,81],"blocks.":[16],"We":[17,31],"propose":[18],"and":[19,23,92,121],"study":[20],"block":[21,90],"diagonal":[22,91],"Schur":[24,93],"complement":[25,94],"preconditioners":[26,95],"for":[27,34,48],"such":[28,89],"matrices.":[30],"show":[32],"that":[33],"some":[35],"matrices,":[37],"spectra":[39],"preconditioned":[42,76],"matrices":[43],"are":[44,124,128],"uniformly":[45],"bounded":[46],"except":[47],"a":[49,108],"fixed":[50,56],"number":[51,57],"outliers":[53],"where":[54],"depends":[58],"only":[59],"on":[60],"block.":[65],"Hence,":[66],"conjugate":[67],"gradient":[68],"type":[69],"methods,":[70],"when":[71],"applied":[72],"to":[73,112,130],"solving":[74],"these":[75],"blocks,":[82],"converge":[83],"very":[84],"fast.":[85],"Recursive":[86],"computation":[87],"is":[96],"considered":[97],"by":[98],"using":[99],"nice":[101],"matrix":[102],"representation":[103],"inverse":[106],"matrix.":[110],"Applications":[111],"arising":[115],"from":[116],"least":[117],"squares":[118],"filtering":[119],"problems":[120],"queueing":[122],"networks":[123],"presented.":[125],"Numerical":[126],"examples":[127],"given":[129],"demonstrate":[131],"effectiveness":[133],"proposed":[136],"method.":[137]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}