{"id":"https://openalex.org/W2094520331","doi":"https://doi.org/10.1080/00207160212121","title":"Existence and Stability of Choleski Q.I.F. for Symmetric Linear Systems","display_name":"Existence and Stability of Choleski Q.I.F. for Symmetric Linear Systems","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2094520331","doi":"https://doi.org/10.1080/00207160212121","mag":"2094520331"},"language":"en","primary_location":{"id":"doi:10.1080/00207160212121","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160212121","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5089200114","display_name":"R. Khazal","orcid":null},"institutions":[{"id":"https://openalex.org/I36721946","display_name":"Kuwait University","ror":"https://ror.org/021e5j056","country_code":"KW","type":"education","lineage":["https://openalex.org/I36721946"]}],"countries":["KW"],"is_corresponding":true,"raw_author_name":"R. R. Khazal","raw_affiliation_strings":["Department of Mathematics and Computer Science , Kuwait University , P.O. Box 5969, Safat, 13060, Kuwait","Department of Mathematics and Computer Science, Kuwait University P.O. Box 5969, Safat 13060, Kuwait#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science , Kuwait University , P.O. Box 5969, Safat, 13060, Kuwait","institution_ids":["https://openalex.org/I36721946"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, Kuwait University P.O. Box 5969, Safat 13060, Kuwait#TAB#","institution_ids":["https://openalex.org/I36721946"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5089200114"],"corresponding_institution_ids":["https://openalex.org/I36721946"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.1559741,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"79","issue":"9","first_page":"1013","last_page":"1025"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987999796867371,"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":0.9987999796867371,"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":0.9937000274658203,"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":0.9927999973297119,"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/mathematics","display_name":"Mathematics","score":0.8256317377090454},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.8195323944091797},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.7347528338432312},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.70614093542099},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.622166097164154},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5365685224533081},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5262880921363831},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.5029758810997009},{"id":"https://openalex.org/keywords/arithmetic-function","display_name":"Arithmetic function","score":0.4983367919921875},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45581215620040894},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.44442230463027954},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.4341799020767212},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.42838191986083984},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3923734426498413},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36586129665374756},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07536789774894714},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07477149367332458},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06751197576522827}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8256317377090454},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.8195323944091797},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.7347528338432312},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.70614093542099},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.622166097164154},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5365685224533081},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5262880921363831},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.5029758810997009},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.4983367919921875},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45581215620040894},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.44442230463027954},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4341799020767212},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.42838191986083984},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3923734426498413},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36586129665374756},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07536789774894714},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07477149367332458},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06751197576522827},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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:10.1080/00207160212121","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160212121","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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":5,"referenced_works":["https://openalex.org/W19209855","https://openalex.org/W2028565542","https://openalex.org/W2030121615","https://openalex.org/W2082196937","https://openalex.org/W2093925907"],"related_works":["https://openalex.org/W1719857135","https://openalex.org/W2349582882","https://openalex.org/W2029431083","https://openalex.org/W2978783905","https://openalex.org/W1980417461","https://openalex.org/W2353317030","https://openalex.org/W40680864","https://openalex.org/W2088694512","https://openalex.org/W2366095940","https://openalex.org/W370913997"],"abstract_inverted_index":{"Recently,":[0],"Evans":[1],"[1]":[2],"has":[3],"given":[4],"a":[5,70],"variant":[6],"of":[7,18,30,34,54,56,65,74,78],"the":[8,16,23,28,35,45,57,62,66,79,84,101,104,109,118,131,137,140],"classical":[9,141],"Choleski":[10,13,41,85,110,132,142],"factorization,":[11],"called":[12],"Q.I.F.,":[14],"for":[15,130,139],"solution":[17],"symmetric":[19,49,122],"linear":[20],"systems.":[21],"In":[22],"present":[24],"paper":[25],"we":[26,106],"address":[27],"questions":[29],"existence":[31,55],"and":[32,103],"stability":[33],"factorization.":[36,143],"We":[37,125],"show":[38,107],"that":[39,108],"Evans'":[40],"Q.I.F.":[42,86,111],"exists":[43],"if":[44,117],"coefficient":[46,80,119],"matrix":[47,120],"is":[48,59,112,121],"positive":[50,123],"definite.":[51,124],"Our":[52],"proof":[53],"factorization":[58],"via":[60],"obtaining":[61],"diagonal":[63],"elements":[64],"factor":[67],"matrices":[68],"in":[69,72,91,98],"closed-form":[71],"terms":[73],"certain":[75],"principal":[76],"minors":[77],"matrix.":[81],"By":[82],"interpreting":[83],"as":[87],"an":[88],"elimination":[89],"procedure":[90],"which":[92],"eliminations":[93],"are":[94],"carried":[95],"out,":[96],"alternately,":[97],"columns":[99],"from":[100],"left":[102],"right,":[105],"also":[113],"(numerically)":[114],"strongly":[115],"stable":[116],"include":[126],"arithmetical":[127],"operations":[128],"counts":[129,138],"Q.I.F.;":[133],"these":[134],"agree":[135],"with":[136]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}