{"id":"https://openalex.org/W2039562885","doi":"https://doi.org/10.1137/040620369","title":"Disc Separation of the Schur Complement of Diagonally Dominant Matrices and Determinantal Bounds","display_name":"Disc Separation of the Schur Complement of Diagonally Dominant Matrices and Determinantal Bounds","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2039562885","doi":"https://doi.org/10.1137/040620369","mag":"2039562885"},"language":"en","primary_location":{"id":"doi:10.1137/040620369","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040620369","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/A5103207599","display_name":"Jianzhou Liu","orcid":"https://orcid.org/0000-0003-1056-0274"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianzhou Liu","raw_affiliation_strings":["Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090138238","display_name":"Fuzhen Zhang","orcid":"https://orcid.org/0000-0002-3414-2037"},"institutions":[{"id":"https://openalex.org/I203088144","display_name":"Nova Southeastern University","ror":"https://ror.org/042bbge36","country_code":"US","type":"education","lineage":["https://openalex.org/I203088144"]},{"id":"https://openalex.org/I32399674","display_name":"Shenyang Normal University","ror":"https://ror.org/05cdfgm80","country_code":"CN","type":"education","lineage":["https://openalex.org/I32399674"]}],"countries":["CN","US"],"is_corresponding":true,"raw_author_name":"Fuzhen Zhang","raw_affiliation_strings":["Division of Math, Science and Technology, Nova Southeastern University, 3301 College Ave., Fort Lauderdale, FL 33314, and School of Mathematics and Systems Science,","Shenyang Normal University, Shenyang, Liaoning 110034, China"],"affiliations":[{"raw_affiliation_string":"Division of Math, Science and Technology, Nova Southeastern University, 3301 College Ave., Fort Lauderdale, FL 33314, and School of Mathematics and Systems Science,","institution_ids":["https://openalex.org/I203088144"]},{"raw_affiliation_string":"Shenyang Normal University, Shenyang, Liaoning 110034, China","institution_ids":["https://openalex.org/I32399674"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090138238"],"corresponding_institution_ids":["https://openalex.org/I203088144","https://openalex.org/I32399674"],"apc_list":null,"apc_paid":null,"fwci":1.0099,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.77178921,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"27","issue":"3","first_page":"665","last_page":"674"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/diagonally-dominant-matrix","display_name":"Diagonally dominant matrix","score":0.9237595200538635},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8667862415313721},{"id":"https://openalex.org/keywords/schur-complement","display_name":"Schur complement","score":0.8129695653915405},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5689942836761475},{"id":"https://openalex.org/keywords/schurs-theorem","display_name":"Schur's theorem","score":0.5554903149604797},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5521537065505981},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.5200914144515991},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4740687906742096},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.4404180347919464},{"id":"https://openalex.org/keywords/m-matrix","display_name":"M-matrix","score":0.4361770749092102},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4279508888721466},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22926801443099976},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.0895533561706543},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.0713982880115509},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05560505390167236}],"concepts":[{"id":"https://openalex.org/C84507854","wikidata":"https://www.wikidata.org/wiki/Q952222","display_name":"Diagonally dominant matrix","level":3,"score":0.9237595200538635},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8667862415313721},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.8129695653915405},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5689942836761475},{"id":"https://openalex.org/C29701004","wikidata":"https://www.wikidata.org/wiki/Q1786292","display_name":"Schur's theorem","level":5,"score":0.5554903149604797},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5521537065505981},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.5200914144515991},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4740687906742096},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4404180347919464},{"id":"https://openalex.org/C61987429","wikidata":"https://www.wikidata.org/wiki/Q3064355","display_name":"M-matrix","level":3,"score":0.4361770749092102},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4279508888721466},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22926801443099976},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.0895533561706543},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.0713982880115509},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05560505390167236},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"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/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"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:10.1137/040620369","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040620369","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:nsuworks.nova.edu:math_facarticles-1050","is_oa":false,"landing_page_url":"https://nsuworks.nova.edu/math_facarticles/51","pdf_url":null,"source":{"id":"https://openalex.org/S4377196410","display_name":"NSUWorks (Nova Southeastern University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I203088144","host_organization_name":"Nova Southeastern University","host_organization_lineage":["https://openalex.org/I203088144"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Faculty Articles","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311589","display_name":"Nova Southeastern University","ror":"https://ror.org/042bbge36"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W147084376","https://openalex.org/W391578156","https://openalex.org/W1488435683","https://openalex.org/W1497459357","https://openalex.org/W1500921805","https://openalex.org/W1542938076","https://openalex.org/W1602049633","https://openalex.org/W1789593150","https://openalex.org/W1974430377","https://openalex.org/W1980848665","https://openalex.org/W1981662169","https://openalex.org/W1989297607","https://openalex.org/W2006008787","https://openalex.org/W2059276620","https://openalex.org/W2059575218","https://openalex.org/W2137880375","https://openalex.org/W2138110186","https://openalex.org/W2610857016","https://openalex.org/W2735263270","https://openalex.org/W4206307023","https://openalex.org/W4213089875"],"related_works":["https://openalex.org/W2522358176","https://openalex.org/W3023764490","https://openalex.org/W2022236900","https://openalex.org/W2152313758","https://openalex.org/W2106849510","https://openalex.org/W2564460214","https://openalex.org/W4311362761","https://openalex.org/W2589912672","https://openalex.org/W2126343135","https://openalex.org/W2034395027"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,7,20,23,37,45,57],"Gersgorin":[3],"disc":[4],"separation":[5,21],"from":[6],"origin":[8],"for":[9,56],"(doubly)":[10,28],"diagonally":[11,29,60],"dominant":[12,30,61],"matrices":[13],"and":[14,49,53],"their":[15],"Schur":[16,24],"complements,":[17],"showing":[18],"that":[19,35],"of":[22,26,36,47,59],"complement":[25],"a":[27],"matrix":[31],"is":[32],"greater":[33],"than":[34],"original":[38],"grand":[39],"matrix.":[40],"As":[41],"application":[42],"we":[43],"discuss":[44],"localization":[46],"eigenvalues":[48],"present":[50],"some":[51],"upper":[52],"lower":[54],"bounds":[55],"determinant":[58],"matrices.":[62]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}