{"id":"https://openalex.org/W2233293187","doi":"https://doi.org/10.2478/cmam-2009-0013","title":"Positive Definite Hankel Matrices Using Cholesky Factorization","display_name":"Positive Definite Hankel Matrices Using Cholesky Factorization","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2233293187","doi":"https://doi.org/10.2478/cmam-2009-0013","mag":"2233293187"},"language":"en","primary_location":{"id":"doi:10.2478/cmam-2009-0013","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2009-0013","pdf_url":"https://www.degruyter.com/downloadpdf/journals/cmam/9/3/article-p221.pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.degruyter.com/downloadpdf/journals/cmam/9/3/article-p221.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002577873","display_name":"Suliman Al\u2010Homidan","orcid":"https://orcid.org/0000-0002-5998-0635"},"institutions":[{"id":"https://openalex.org/I134085113","display_name":"King Fahd University of Petroleum and Minerals","ror":"https://ror.org/03yez3163","country_code":"SA","type":"education","lineage":["https://openalex.org/I134085113"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"S. Al-homidan","raw_affiliation_strings":["1Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"1Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia","institution_ids":["https://openalex.org/I134085113"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017870575","display_name":"Mohammed Alshahrani","orcid":"https://orcid.org/0000-0002-1367-646X"},"institutions":[{"id":"https://openalex.org/I134085113","display_name":"King Fahd University of Petroleum and Minerals","ror":"https://ror.org/03yez3163","country_code":"SA","type":"education","lineage":["https://openalex.org/I134085113"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"M. Alshahrani","raw_affiliation_strings":["1Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"1Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia","institution_ids":["https://openalex.org/I134085113"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002577873"],"corresponding_institution_ids":["https://openalex.org/I134085113"],"apc_list":null,"apc_paid":null,"fwci":0.3428,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.64662804,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"9","issue":"3","first_page":"221","last_page":"225"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9854999780654907,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9828000068664551,"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/cholesky-decomposition","display_name":"Cholesky decomposition","score":0.9779676795005798},{"id":"https://openalex.org/keywords/incomplete-cholesky-factorization","display_name":"Incomplete Cholesky factorization","score":0.914337694644928},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.840989351272583},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6909662485122681},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6744861602783203},{"id":"https://openalex.org/keywords/hankel-matrix","display_name":"Hankel matrix","score":0.642743706703186},{"id":"https://openalex.org/keywords/minimum-degree-algorithm","display_name":"Minimum degree algorithm","score":0.628735363483429},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48345503211021423},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33092907071113586},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31756824254989624},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22505763173103333},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1814042031764984},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.11227509379386902},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08165115118026733}],"concepts":[{"id":"https://openalex.org/C34727166","wikidata":"https://www.wikidata.org/wiki/Q515375","display_name":"Cholesky decomposition","level":3,"score":0.9779676795005798},{"id":"https://openalex.org/C44363057","wikidata":"https://www.wikidata.org/wiki/Q6015160","display_name":"Incomplete Cholesky factorization","level":4,"score":0.914337694644928},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.840989351272583},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6909662485122681},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6744861602783203},{"id":"https://openalex.org/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.642743706703186},{"id":"https://openalex.org/C46085209","wikidata":"https://www.wikidata.org/wiki/Q17098969","display_name":"Minimum degree algorithm","level":5,"score":0.628735363483429},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48345503211021423},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33092907071113586},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31756824254989624},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22505763173103333},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1814042031764984},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.11227509379386902},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08165115118026733},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2478/cmam-2009-0013","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2009-0013","pdf_url":"https://www.degruyter.com/downloadpdf/journals/cmam/9/3/article-p221.pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.2478/cmam-2009-0013","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2009-0013","pdf_url":"https://www.degruyter.com/downloadpdf/journals/cmam/9/3/article-p221.pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322323","display_name":"King Fahd University of Petroleum and Minerals","ror":"https://ror.org/03yez3163"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2233293187.pdf","grobid_xml":"https://content.openalex.org/works/W2233293187.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1609583274","https://openalex.org/W1828046956","https://openalex.org/W1977701268","https://openalex.org/W2001371760","https://openalex.org/W2005229894","https://openalex.org/W2046921424","https://openalex.org/W2089638310","https://openalex.org/W6629495966"],"related_works":["https://openalex.org/W4255359805","https://openalex.org/W2504688771","https://openalex.org/W2075453197","https://openalex.org/W2057318281","https://openalex.org/W2924783966","https://openalex.org/W1482750774","https://openalex.org/W2233293187","https://openalex.org/W2394244817","https://openalex.org/W2093365458","https://openalex.org/W2369049787"],"abstract_inverted_index":{"Abstract":[0],"Real":[1],"positive":[2,29],"definite":[3,30],"Hankel":[4,31],"matrices":[5,32],"arise":[6],"in":[7],"many":[8],"important":[9],"applications.":[10],"They":[11],"have":[12],"spectral":[13],"condition":[14],"numbers":[15],"which":[16],"exponentially":[17],"increase":[18],"with":[19,51],"their":[20],"orders.":[21],"We":[22],"give":[23],"a":[24],"structural":[25],"algorithm":[26],"for":[27,39],"finding":[28],"using":[33],"the":[34],"Cholesky":[35],"factorization,":[36],"compute":[37],"it":[38],"orders":[40],"less":[41],"than":[42],"or":[43],"equal":[44],"to":[45],"30,":[46],"and":[47],"compare":[48],"our":[49],"result":[50],"earlier":[52],"results.":[53]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
