{"id":"https://openalex.org/W1973665828","doi":"https://doi.org/10.1137/s0895479892230973","title":"Some Results on Structure Prediction in Sparse $QR$ Factorization","display_name":"Some Results on Structure Prediction in Sparse $QR$ Factorization","publication_year":1996,"publication_date":"1996-04-01","ids":{"openalex":"https://openalex.org/W1973665828","doi":"https://doi.org/10.1137/s0895479892230973","mag":"1973665828"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479892230973","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479892230973","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/A5056131016","display_name":"Esmond Ng","orcid":"https://orcid.org/0000-0002-4535-6348"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Esmond G. Ng","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5050129306","display_name":"Barry W. Peyton","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Barry W. Peyton","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056131016"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0837,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.75012892,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"17","issue":"2","first_page":"443","last_page":"459"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9976999759674072,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9976999759674072,"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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9965000152587891,"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/triangular-matrix","display_name":"Triangular matrix","score":0.8323075771331787},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8163132667541504},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7560885548591614},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.7315351366996765},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.68206787109375},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5512248277664185},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5465973019599915},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.5360031723976135},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.46113646030426025},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40465354919433594},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17269837856292725},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15671896934509277},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14355885982513428},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13394832611083984},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.12285968661308289},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.07776665687561035},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07133188843727112},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05636817216873169}],"concepts":[{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.8323075771331787},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8163132667541504},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7560885548591614},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.7315351366996765},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.68206787109375},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5512248277664185},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5465973019599915},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.5360031723976135},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.46113646030426025},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40465354919433594},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17269837856292725},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15671896934509277},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14355885982513428},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13394832611083984},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.12285968661308289},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.07776665687561035},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07133188843727112},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05636817216873169},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895479892230973","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479892230973","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":15,"referenced_works":["https://openalex.org/W133977063","https://openalex.org/W1969710496","https://openalex.org/W1972859808","https://openalex.org/W1981885118","https://openalex.org/W1984958506","https://openalex.org/W2005687287","https://openalex.org/W2015045768","https://openalex.org/W2028495395","https://openalex.org/W2046020107","https://openalex.org/W2063292248","https://openalex.org/W2069792133","https://openalex.org/W2077309453","https://openalex.org/W2091978199","https://openalex.org/W2093992309","https://openalex.org/W2141025928"],"related_works":["https://openalex.org/W2137261070","https://openalex.org/W2065280300","https://openalex.org/W2145716913","https://openalex.org/W4300433781","https://openalex.org/W2056480844","https://openalex.org/W2006502019","https://openalex.org/W2950485393","https://openalex.org/W177315822","https://openalex.org/W2051936539","https://openalex.org/W2021437037"],"abstract_inverted_index":{"In":[0,97],"$QR$":[1,266],"factorization":[2,47,54],"of":[3,40,66,86,95,110,121,129,134,139,157,187,201],"an":[4,24,79,114],"$m":[5,25],"\\times":[6,26],"n$":[7,27],"matrix":[8,30,127,248],"$A\\,":[9],"(":[10],"m":[11],"\\geq":[12],"n":[13,132],")$,":[14],"the":[15,34,38,46,63,83,92,107,118,126,130,140,145,153,158,181,184,192,198,215,261,265],"orthogonal":[16],"factor":[17],"Q":[18],"is":[19,42,48,75,143,150,168,219,222,257],"often":[20,49],"stored":[21],"implicitly":[22],"as":[23,33],"lower":[28,154],"trapezoidal":[29,155],"W,":[31],"known":[32],"Householder":[35],"matrix.":[36],"When":[37],"sparsity":[39],"A":[41,167,218],"to":[43,112,152,208],"be":[44,125],"exploited,":[45],"preceded":[50],"by":[51,77,264],"a":[52,58,102,245],"symbolic":[53],"step,":[55],"which":[56,62],"computes":[57],"data":[59],"structure":[60,85,94,109,120,149,200],"in":[61,214,223,260],"nonzero":[64,84,93,108,119,185,199],"entries":[65],"W":[67,111,188],"and":[68,72,171,189,228],"R":[69],"are":[70,191],"computed":[71],"stored.":[73],"This":[74],"achieved":[76],"computing":[78],"upper":[80,104,115,212,225,251],"bound":[81,105,116,142,146,159],"on":[82,91,106,117,147,160,176,183,197,233],"these":[87],"factors,":[88],"based":[89,195],"solely":[90,196],"A.":[96,202],"this":[98,206],"paper":[99],"we":[100,238],"use":[101,205],"well-known":[103],"obtain":[113,209],"Q.":[122,135],"Let":[123],"U":[124,190],"consisting":[128],"first":[131],"columns":[133],"One":[136],"interesting":[137],"feature":[138],"new":[141],"that":[144,165,240,255],"W\u2019s":[148],"identical":[151],"part":[156],"U\u2019s":[161],"structure.":[162],"We":[163,203],"show":[164,239],"if":[166],"strong":[169],"Hall":[170,247],"has":[172,229],"no":[173,230,258],"zero":[174,231],"entry":[175,232],"its":[177,234],"main":[178,235],"diagonal,":[179],"then":[180,204],"bounds":[182,213],"structures":[186],"smallest":[193,211],"possible":[194],"result":[207],"corresponding":[210],"case":[216],"where":[217],"weak":[220,246],"Hall,":[221],"block":[224,250],"triangular":[226,252],"form,":[227],"diagonal.":[236],"Finally,":[237],"one":[241],"can":[242],"always":[243],"reorder":[244],"into":[249],"form":[253],"so":[254],"there":[256],"increase":[259],"fill":[262],"incurred":[263],"factorization.":[267]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
