{"id":"https://openalex.org/W2041095828","doi":"https://doi.org/10.1080/00207160008804904","title":"Fast qz decomposition and its applications","display_name":"Fast qz decomposition and its applications","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2041095828","doi":"https://doi.org/10.1080/00207160008804904","mag":"2041095828"},"language":"en","primary_location":{"id":"doi:10.1080/00207160008804904","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160008804904","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/A5101876243","display_name":"Changjun Li","orcid":"https://orcid.org/0000-0002-7265-4893"},"institutions":[{"id":"https://openalex.org/I87182695","display_name":"Universidad del Noreste","ror":"https://ror.org/02ahky613","country_code":"MX","type":"education","lineage":["https://openalex.org/I87182695"]},{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN","MX"],"is_corresponding":true,"raw_author_name":"Changjun Li","raw_affiliation_strings":["Northeastern University","Dept. of Math, Northeastern University, Shenyang, 110006, ChinaOpen Lab of, CAD/CAM Tech. For Avanced Manufacturing, Academia Sinica, China"],"affiliations":[{"raw_affiliation_string":"Northeastern University","institution_ids":["https://openalex.org/I87182695"]},{"raw_affiliation_string":"Dept. of Math, Northeastern University, Shenyang, 110006, ChinaOpen Lab of, CAD/CAM Tech. For Avanced Manufacturing, Academia Sinica, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103518679","display_name":"D. J. Evans","orcid":null},"institutions":[{"id":"https://openalex.org/I52590639","display_name":"Nottingham Trent University","ror":"https://ror.org/04xyxjd90","country_code":"GB","type":"education","lineage":["https://openalex.org/I52590639"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"David J Evans","raw_affiliation_strings":["Nottingham Trent University","Dept. of Computing, Nottingham Trent University, Nottingham, NG1 4BU, UK"],"affiliations":[{"raw_affiliation_string":"Nottingham Trent University","institution_ids":["https://openalex.org/I52590639"]},{"raw_affiliation_string":"Dept. of Computing, Nottingham Trent University, Nottingham, NG1 4BU, UK","institution_ids":["https://openalex.org/I52590639"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101876243"],"corresponding_institution_ids":["https://openalex.org/I87182695","https://openalex.org/I9224756"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16391236,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"73","issue":"3","first_page":"371","last_page":"387"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987000226974487,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9944000244140625,"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/computation","display_name":"Computation","score":0.5474739670753479},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5049605965614319},{"id":"https://openalex.org/keywords/foundation","display_name":"Foundation (evidence)","score":0.5003414154052734},{"id":"https://openalex.org/keywords/china","display_name":"China","score":0.45548927783966064},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43325936794281006},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4137466251850128},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39953774213790894},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37488722801208496},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3319241404533386},{"id":"https://openalex.org/keywords/history","display_name":"History","score":0.124549001455307},{"id":"https://openalex.org/keywords/archaeology","display_name":"Archaeology","score":0.10609737038612366}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5474739670753479},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5049605965614319},{"id":"https://openalex.org/C2780966255","wikidata":"https://www.wikidata.org/wiki/Q5474306","display_name":"Foundation (evidence)","level":2,"score":0.5003414154052734},{"id":"https://openalex.org/C191935318","wikidata":"https://www.wikidata.org/wiki/Q148","display_name":"China","level":2,"score":0.45548927783966064},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43325936794281006},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4137466251850128},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39953774213790894},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37488722801208496},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3319241404533386},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.124549001455307},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.10609737038612366},{"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160008804904","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160008804904","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1974732569","https://openalex.org/W1991352052","https://openalex.org/W2036050714","https://openalex.org/W2042801519","https://openalex.org/W2798909945"],"related_works":["https://openalex.org/W2371896437","https://openalex.org/W2379273257","https://openalex.org/W2984546736","https://openalex.org/W2359511101","https://openalex.org/W2132682661","https://openalex.org/W1572523360","https://openalex.org/W2324973813","https://openalex.org/W2386767533","https://openalex.org/W2067352679","https://openalex.org/W1578200463"],"abstract_inverted_index":{"Abstract":[0],"The":[1,51],"ability":[2],"to":[3,34,41,46,109],"introduce":[4],"zeros":[5],"in":[6,18,31,39],"a":[7,47],"selective":[8],"fashion":[9],"makes":[10],"the":[11,43,56,70,78,82,89,94,101,104,110,119],"Givens":[12,29,127],"Rotations":[13,30],"an":[14],"important":[15],"zeroing":[16],"tool":[17],"certain":[19],"structured":[20],"matrix":[21,45],"problems.":[22],"Evans":[23],"and":[24,60,92,118,138,160,188,217],"Yalamov":[25],"[2]":[26],"combined":[27],"two":[28,36],"one":[32],"step":[33],"annihilate":[35],"elements":[37],"simultaneously":[38],"order":[40],"transform":[42],"original":[44],"\u201cZ\u201d":[48],"form":[49],"pattern.":[50],"composite":[52],"scheme":[53],"was":[54,149,177,206],"called":[55],"QZ":[57,83,106],"decomposition":[58,84,107],"method":[59,108],"is":[61,67,85],"suitable":[62],"for":[63],"parallel":[64,139],"computation,":[65],"which":[66,87],"confirmed":[68],"by":[69,98,151,179,208],"numerical":[71],"results":[72],"[1].":[73],"In":[74],"this":[75],"paper,":[76],"firstly":[77],"fast":[79,105],"computation":[80],"of":[81,96,103,113,131,155,164,167,183,192,195,212,221,224],"given,":[86],"eliminates":[88],"square":[90],"roots":[91],"reduces":[93],"number":[95],"multiplications":[97],"37.5%.":[99],"Finally,":[100],"applications":[102],"linear":[111],"system":[112,130],"equations,":[114],"least":[115,121,135],"squares":[116,122,133,136],"problem":[117,123,137],"weighted":[120],"are":[124],"considered.":[125],"Keywords:":[126],"rotationsQZ":[128],"decompositionlinear":[129],"equationsleast":[132],"problemweighted":[134],"computationAMS":[140],"Subject":[141],"clasification:":[142],"65F1065F20C.R.":[143],"Categories:":[144],"G.1.3":[145],"\u2217This":[146,174,203],"author's":[147,175,204],"work":[148,176,205],"supported":[150,178,207],"Natural":[152,161,180,189,209,218],"Science":[153,162,181,190,210,219],"Foundation":[154,163,182,191,211,220],"China":[156,168,184,196,213,225],"(Grant":[157,169,185,197,214,226],"no.":[158,170,186,198,215,227],"19871011),":[159,187,216],"Liaoning":[165,193,222],"Province":[166,194,223],"962172)":[171,199,228],"\u2020Correasponding":[172,200,229],"author":[173,201,230],"Notes":[202]},"counts_by_year":[],"updated_date":"2026-03-07T13:37:22.277990","created_date":"2025-10-10T00:00:00"}