{"id":"https://openalex.org/W2020329636","doi":"https://doi.org/10.1137/s0895479894267689","title":"An Operator Relation of the Ussor and the Jacobi Iteration Matrices of a <i>p</i>-Cyclic Matrix","display_name":"An Operator Relation of the Ussor and the Jacobi Iteration Matrices of a <i>p</i>-Cyclic Matrix","publication_year":1996,"publication_date":"1996-07-01","ids":{"openalex":"https://openalex.org/W2020329636","doi":"https://doi.org/10.1137/s0895479894267689","mag":"2020329636"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479894267689","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479894267689","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":true,"raw_author_name":"Dimitrios Noutsos","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008198354"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.14601728,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"3","first_page":"515","last_page":"529"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T11476","display_name":"Graph theory and applications","score":0.9836999773979187,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9707000255584717,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8626327514648438},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6411876082420349},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.5962556600570679},{"id":"https://openalex.org/keywords/jacobi-operator","display_name":"Jacobi operator","score":0.5846630334854126},{"id":"https://openalex.org/keywords/jacobi-method","display_name":"Jacobi method","score":0.568308413028717},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5298371315002441},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5250266194343567},{"id":"https://openalex.org/keywords/permutation-matrix","display_name":"Permutation matrix","score":0.4972701370716095},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.49520888924598694},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3716827929019928},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3597278594970703},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33834588527679443},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2650133967399597},{"id":"https://openalex.org/keywords/jacobi-polynomials","display_name":"Jacobi polynomials","score":0.2278733253479004},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.08794799447059631},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06057846546173096}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8626327514648438},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6411876082420349},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.5962556600570679},{"id":"https://openalex.org/C633612","wikidata":"https://www.wikidata.org/wiki/Q81192","display_name":"Jacobi operator","level":4,"score":0.5846630334854126},{"id":"https://openalex.org/C67923128","wikidata":"https://www.wikidata.org/wiki/Q1481893","display_name":"Jacobi method","level":2,"score":0.568308413028717},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5298371315002441},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5250266194343567},{"id":"https://openalex.org/C84140500","wikidata":"https://www.wikidata.org/wiki/Q851512","display_name":"Permutation matrix","level":3,"score":0.4972701370716095},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.49520888924598694},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3716827929019928},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3597278594970703},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33834588527679443},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2650133967399597},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.2278733253479004},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.08794799447059631},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06057846546173096},{"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/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},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479894267689","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479894267689","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1972616929","https://openalex.org/W1973193879","https://openalex.org/W1973963848","https://openalex.org/W1992653386","https://openalex.org/W2004944273","https://openalex.org/W2016694817","https://openalex.org/W2020888690","https://openalex.org/W2023050554","https://openalex.org/W2050488651","https://openalex.org/W2052482903","https://openalex.org/W2076220511","https://openalex.org/W2079557221","https://openalex.org/W2083115625","https://openalex.org/W2100647500","https://openalex.org/W2120883753","https://openalex.org/W2569133694","https://openalex.org/W4213214460","https://openalex.org/W4299343067"],"related_works":["https://openalex.org/W967419144","https://openalex.org/W3146790254","https://openalex.org/W183135790","https://openalex.org/W2381799323","https://openalex.org/W2077876398","https://openalex.org/W1730197359","https://openalex.org/W2275366383","https://openalex.org/W2182578416","https://openalex.org/W2212994749","https://openalex.org/W2020329636"],"abstract_inverted_index":{"Let":[0],"the":[1,7,20,47,52,57,70,75,89,97,109,112,122,125,133],"Jacobi":[2,76],"matrix":[3,63,77,94],"B":[4,78,105],"associated":[5],"with":[6],"linear":[8],"system":[9,127],"$Ax":[10],"=":[11,24],"b$":[12],"be":[13],"a":[14,116],"weakly":[15],"cyclic":[16,21],"matrix,":[17],"generated":[18],"by":[19,39,82],"permutation":[22],"$\\sigma":[23],"(":[25],"\\sigma":[26],"_1":[27],",\\sigma":[28,32],"_2":[29],",":[30],"\\cdots":[31],"_p":[33],")$":[34],"as":[35],"this":[36,87],"is":[37,106,128,139],"defined":[38],"Li":[40],"and":[41,69,84,104,115],"Varga.":[42],"The":[43,130],"same":[44],"authors":[45],"derived":[46],"corresponding":[48],"functional":[49],"equation":[50],"connecting":[51,96],"eigenvalues":[53,71],"$\\lambda":[54],"$":[55,68,73,103],"of":[56,74,91,111,124,135],"unsymmetric":[58],"successive":[59],"overrelaxation":[60],"(USSOR)":[61],"iteration":[62],"$T_{\\omega":[64,99],"\\hat":[65,100],"\\omega":[66,101],"}":[67,102],"$\\mu":[72],"extending":[79],"previous":[80],"results":[81],"Gong":[83],"Cal.":[85],"In":[86],"paper,":[88],"validity":[90],"an":[92],"analogous":[93],"relationship":[95],"operators":[98],"proved.":[107],"Moreover,":[108],"\u201cequivalence\u201d":[110],"USSOR":[113],"method":[114,120],"certain":[117],"two-parametric":[118],"p-step":[119],"for":[121,132],"solution":[123],"initial":[126],"established.":[129],"tool":[131],"proof":[134],"our":[136],"main":[137],"result":[138],"elementary":[140],"graph":[141],"theory.":[142]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
