{"id":"https://openalex.org/W1968822119","doi":"https://doi.org/10.1145/2168773.2168780","title":"Algorithm 918","display_name":"Algorithm 918","publication_year":2012,"publication_date":"2012-04-01","ids":{"openalex":"https://openalex.org/W1968822119","doi":"https://doi.org/10.1145/2168773.2168780","mag":"1968822119"},"language":"en","primary_location":{"id":"doi:10.1145/2168773.2168780","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2168773.2168780","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","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/A5066895480","display_name":"Miloud Sadkane","orcid":"https://orcid.org/0000-0002-7712-7048"},"institutions":[{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Miloud Sadkane","raw_affiliation_strings":["University of Brest, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Brest, France","institution_ids":["https://openalex.org/I161929037"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056764070","display_name":"Ahmed Touhami","orcid":null},"institutions":[{"id":"https://openalex.org/I4210145365","display_name":"Universit\u00e9 Hassan 1er","ror":"https://ror.org/03cdvht47","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210145365"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Ahmed Touhami","raw_affiliation_strings":["Hassan 1st University, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hassan 1st University, Morocco","institution_ids":["https://openalex.org/I4210145365"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6946,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69600276,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"38","issue":"3","first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.8108000159263611,"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":0.8108000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/projector","display_name":"Projector","score":0.7628903388977051},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7570990920066833},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.66021728515625},{"id":"https://openalex.org/keywords/ellipse","display_name":"Ellipse","score":0.6331467032432556},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.6103173494338989},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.5950580835342407},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.49979090690612793},{"id":"https://openalex.org/keywords/eigendecomposition-of-a-matrix","display_name":"Eigendecomposition of a matrix","score":0.4804344177246094},{"id":"https://openalex.org/keywords/pencil","display_name":"Pencil (optics)","score":0.4588705897331238},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4436095952987671},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42964833974838257},{"id":"https://openalex.org/keywords/matlab","display_name":"MATLAB","score":0.4217890501022339},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.41560837626457214},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37618887424468994},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37185361981391907},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3508882522583008},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2384015917778015},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1861020028591156},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.11981675028800964},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10864555835723877},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.07851627469062805}],"concepts":[{"id":"https://openalex.org/C2776865275","wikidata":"https://www.wikidata.org/wiki/Q311666","display_name":"Projector","level":2,"score":0.7628903388977051},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7570990920066833},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.66021728515625},{"id":"https://openalex.org/C74261601","wikidata":"https://www.wikidata.org/wiki/Q40112","display_name":"Ellipse","level":2,"score":0.6331467032432556},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.6103173494338989},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.5950580835342407},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.49979090690612793},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.4804344177246094},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.4588705897331238},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4436095952987671},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42964833974838257},{"id":"https://openalex.org/C2780365114","wikidata":"https://www.wikidata.org/wiki/Q169478","display_name":"MATLAB","level":2,"score":0.4217890501022339},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.41560837626457214},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37618887424468994},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37185361981391907},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3508882522583008},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2384015917778015},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1861020028591156},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.11981675028800964},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10864555835723877},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.07851627469062805},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2168773.2168780","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2168773.2168780","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.5600000023841858}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W151868298","https://openalex.org/W179690054","https://openalex.org/W579600426","https://openalex.org/W1979674329","https://openalex.org/W2005999980","https://openalex.org/W2023413246","https://openalex.org/W2034846432","https://openalex.org/W2044019214","https://openalex.org/W2065304801","https://openalex.org/W2082778893","https://openalex.org/W2109704467","https://openalex.org/W2406624004","https://openalex.org/W2617450232","https://openalex.org/W2798813531","https://openalex.org/W4285719527","https://openalex.org/W6659138781"],"related_works":["https://openalex.org/W2366989203","https://openalex.org/W3196517001","https://openalex.org/W2352678454","https://openalex.org/W2013995543","https://openalex.org/W2949824776","https://openalex.org/W2800812882","https://openalex.org/W2547954852","https://openalex.org/W3198360760","https://openalex.org/W2122589520","https://openalex.org/W3138597860"],"abstract_inverted_index":{"Given":[0],"a":[1,10,44,94,130,144,152],"regular":[2],"matrix":[3,98],"pencil":[4],"\u03bb":[5,25,35,68],"B":[6,26,36,69],"--":[7,27,37,70],"A":[8,28,38,71],"and":[9,29],"positively":[11],"oriented":[12],"contour":[13],"\u03b3":[14,30,47,77,142],"in":[15,32,43],"the":[16,19,58,63,74,82,87,101,108,112,123,135,148],"complex":[17],"plane,":[18],"spectral":[20,59,88,113,139],"dichotomy":[21,102,140],"methods":[22,55],"applied":[23],"to":[24],"consist":[31],"determining":[33],"whether":[34],"possesses":[39],"eigenvalues":[40,52,75],"on":[41],"or":[42,151],"neighborhood":[45],"of":[46,67,81,93,111,138],".":[48,78,116],"When":[49],"no":[50],"such":[51],"exist,":[53],"these":[54],"compute":[56],"iteratively":[57],"projector":[60,83,114],"P":[61,115],"onto":[62],"right":[64],"deflating":[65],"subspace":[66],"associated":[72],"with":[73],"inside/outside":[76],"The":[79,117],"computation":[80],"is":[84,143],"accompanied":[85],"by":[86],"norm":[89],"||":[90,92,119,121],"H":[91,99,120],"Hermitian":[95],"positive":[96],"definite":[97],"called":[100],"condition":[103],"number":[104],",":[105],"which":[106],"indicates":[107],"numerical":[109],"quality":[110],"smaller":[118],"is,":[122],"better":[124],"this":[125],"quality.":[126],"This":[127],"article":[128],"presents":[129],"MATLAB":[131],"program":[132],"(specdicho)":[133],"implementing":[134],"main":[136],"types":[137],"where":[141],"circle,":[145],"an":[146],"ellipse,":[147],"imaginary":[149],"axis":[150],"parabola.":[153]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}