{"id":"https://openalex.org/W1964578872","doi":"https://doi.org/10.1137/050633032","title":"MIQR: A Multilevel Incomplete QR Preconditioner for Large Sparse Least\u2010Squares Problems","display_name":"MIQR: A Multilevel Incomplete QR Preconditioner for Large Sparse Least\u2010Squares Problems","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1964578872","doi":"https://doi.org/10.1137/050633032","mag":"1964578872"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/050633032","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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://www.cs.umn.edu/~saad/PDF/umsi-2005-107.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100368048","display_name":"Na Li","orcid":"https://orcid.org/0000-0001-9545-3050"},"institutions":[{"id":"https://openalex.org/I4210101327","display_name":"Twin Cities Orthopedics","ror":"https://ror.org/01en4s460","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210101327"]},{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Na Li","raw_affiliation_strings":["University of Minnesota Twin Cities"],"affiliations":[{"raw_affiliation_string":"University of Minnesota Twin Cities","institution_ids":["https://openalex.org/I4210101327","https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016419713","display_name":"Yousef Saad","orcid":"https://orcid.org/0000-0002-8614-5360"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yousef Saad","raw_affiliation_strings":["Computer Science and Engineering"],"affiliations":[{"raw_affiliation_string":"Computer Science and Engineering","institution_ids":[]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.606,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":37,"citation_normalized_percentile":{"value":0.876678,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":92},"biblio":{"volume":"28","issue":"2","first_page":"524","last_page":"550"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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":0.9967,"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":0.9917,"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/qr-decomposition","display_name":"QR decomposition","score":0.9158229},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.64061785},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5328574},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.42476684},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41308796}],"concepts":[{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.9158229},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.847045},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6614408},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.64061785},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.617069},{"id":"https://openalex.org/C134978465","wikidata":"https://www.wikidata.org/wiki/Q1654069","display_name":"Incomplete LU factorization","level":4,"score":0.5992087},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5328574},{"id":"https://openalex.org/C44363057","wikidata":"https://www.wikidata.org/wiki/Q6015160","display_name":"Incomplete Cholesky factorization","level":4,"score":0.49830103},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4407626},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.43115306},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.43095428},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.42476684},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4229189},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.41599685},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41308796},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39928016},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30519983},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.24941134},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24262354},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.22353661},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08912015},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.065951675},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/050633032","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":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.131.7654","pdf_url":"http://www.cs.umn.edu/~saad/PDF/umsi-2005-107.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.131.7654","pdf_url":"http://www.cs.umn.edu/~saad/PDF/umsi-2005-107.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":32,"referenced_works":["https://openalex.org/W1488292267","https://openalex.org/W1502919101","https://openalex.org/W1548791757","https://openalex.org/W1963564197","https://openalex.org/W1974421439","https://openalex.org/W1980416455","https://openalex.org/W1995561370","https://openalex.org/W2000165536","https://openalex.org/W2006452217","https://openalex.org/W2007903522","https://openalex.org/W2008315167","https://openalex.org/W2009441498","https://openalex.org/W2010315317","https://openalex.org/W2013336356","https://openalex.org/W2023567863","https://openalex.org/W2024615455","https://openalex.org/W2026041872","https://openalex.org/W2027532376","https://openalex.org/W2030942503","https://openalex.org/W2032052535","https://openalex.org/W2043448909","https://openalex.org/W2044557804","https://openalex.org/W2051633585","https://openalex.org/W2066610136","https://openalex.org/W2073555064","https://openalex.org/W2078637543","https://openalex.org/W2081135029","https://openalex.org/W2089979798","https://openalex.org/W2097897435","https://openalex.org/W2250107905","https://openalex.org/W3000211808","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2966631139","https://openalex.org/W2809896915","https://openalex.org/W2803869170","https://openalex.org/W2282105799","https://openalex.org/W2157073722","https://openalex.org/W2146296113","https://openalex.org/W1994991343","https://openalex.org/W1987177655","https://openalex.org/W1986651373","https://openalex.org/W1509943448"],"abstract_inverted_index":{"This":[0],"paper":[1],"describes":[2],"a":[3,40,68,84,102],"multilevel":[4,152],"incomplete":[5,88,140,145],"QR":[6,86,89,141],"factorization":[7,18,146],"for":[8,67],"solving":[9],"large":[10],"sparse":[11,25],"least\u2010squares":[12],"problems.":[13],"The":[14,48,77],"algorithm":[15,32],"builds":[16],"the":[17,31,58,62,96,119,122,138,143,149],"by":[19],"exploiting":[20],"structural":[21],"orthogonality":[22],"in":[23,98],"general":[24],"matrices.":[26],"At":[27],"any":[28],"given":[29],"step,":[30],"finds":[33],"an":[34],"independent":[35,59,125],"set":[36,41],"of":[37,42,57,71,105,121,124,127],"columns,":[38],"i.e.,":[39],"columns":[43,50,56],"that":[44],"have":[45],"orthogonal":[46],"patterns.":[47],"other":[49],"are":[51,93,114,131],"then":[52],"block":[53],"orthogonalized":[54],"against":[55],"set,":[60],"and":[61,148],"process":[63],"is":[64,81,118],"repeated":[65],"recursively":[66],"certain":[69],"number":[70],"levels":[72,97],"on":[73],"these":[74,117],"remaining":[75],"columns.":[76,128],"final":[78],"level":[79,104],"matrix":[80],"processed":[82],"with":[83,137],"standard":[85,139],"or":[87],"factorization.":[90],"Dropping":[91],"strategies":[92],"employed":[94],"throughout":[95],"order":[99],"to":[100,110],"maintain":[101],"good":[103],"sparsity.":[106],"A":[107],"few":[108],"improvements":[109],"this":[111,135],"basic":[112],"scheme":[113,136],"explored.":[115],"Among":[116],"relaxation":[120],"requirement":[123],"sets":[126],"Numerical":[129],"tests":[130],"proposed":[132],"which":[133],"compare":[134],"preconditioner,":[142,147],"robust":[144],"algebraic":[150],"recursive":[151],"solver":[153],"(on":[154],"normal":[155],"equations).":[156]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W1964578872","counts_by_year":[{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2025-01-06T10:28:28.358352","created_date":"2016-06-24"}