{"id":"https://openalex.org/W2064473653","doi":"https://doi.org/10.1145/1993886.1993929","title":"Randomized preconditioning of the MBA algorithm","display_name":"Randomized preconditioning of the MBA algorithm","publication_year":2011,"publication_date":"2011-06-08","ids":{"openalex":"https://openalex.org/W2064473653","doi":"https://doi.org/10.1145/1993886.1993929","mag":"2064473653"},"language":"en","primary_location":{"id":"doi:10.1145/1993886.1993929","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1993886.1993929","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 36th international symposium on Symbolic and algebraic computation","raw_type":"proceedings-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/A5056866601","display_name":"Victor Y. Pan","orcid":"https://orcid.org/0000-0002-9819-9358"},"institutions":[{"id":"https://openalex.org/I161301626","display_name":"Lehman College","ror":"https://ror.org/03m908832","country_code":"US","type":"education","lineage":["https://openalex.org/I161301626"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Victor Y. Pan","raw_affiliation_strings":["Lehman College of CUNY, Bronx, NY, USA","Lehman College of CUNY, Bronx, NY, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lehman College of CUNY, Bronx, NY, USA","institution_ids":["https://openalex.org/I161301626"]},{"raw_affiliation_string":"Lehman College of CUNY, Bronx, NY, USA#TAB#","institution_ids":["https://openalex.org/I161301626"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110293006","display_name":"Guoliang Qian","orcid":null},"institutions":[{"id":"https://openalex.org/I121847817","display_name":"The Graduate Center, CUNY","ror":"https://ror.org/00awd9g61","country_code":"US","type":"education","lineage":["https://openalex.org/I121847817"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guoliang Qian","raw_affiliation_strings":["The Graduate Center of CUNY, New York, NY, USA","The Graduate Center of CUNY, New York, NY, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Graduate Center of CUNY, New York, NY, USA","institution_ids":["https://openalex.org/I121847817"]},{"raw_affiliation_string":"The Graduate Center of CUNY, New York, NY, USA#TAB#","institution_ids":["https://openalex.org/I121847817"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007207817","display_name":"Ai-Long Zheng","orcid":null},"institutions":[{"id":"https://openalex.org/I121847817","display_name":"The Graduate Center, CUNY","ror":"https://ror.org/00awd9g61","country_code":"US","type":"education","lineage":["https://openalex.org/I121847817"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ai-Long Zheng","raw_affiliation_strings":["The Graduate Center of CUNY, New York, NY, USA","The Graduate Center of CUNY, New York, NY, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Graduate Center of CUNY, New York, NY, USA","institution_ids":["https://openalex.org/I121847817"]},{"raw_affiliation_string":"The Graduate Center of CUNY, New York, NY, USA#TAB#","institution_ids":["https://openalex.org/I121847817"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9352,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.90930726,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"281","last_page":"288"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9995999932289124,"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":0.9995999932289124,"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/T11716","display_name":"Random Matrices and Applications","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.7063115239143372},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.6490137577056885},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6284760236740112},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5802152156829834},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5096206665039062},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4979715347290039},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4516351819038391},{"id":"https://openalex.org/keywords/randomization","display_name":"Randomization","score":0.42459651827812195},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.413473904132843},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.379604309797287},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32025468349456787},{"id":"https://openalex.org/keywords/randomized-controlled-trial","display_name":"Randomized controlled trial","score":0.22715997695922852},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1261502504348755},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10534307360649109},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08230897784233093}],"concepts":[{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.7063115239143372},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.6490137577056885},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6284760236740112},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5802152156829834},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5096206665039062},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4979715347290039},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4516351819038391},{"id":"https://openalex.org/C204243189","wikidata":"https://www.wikidata.org/wiki/Q1363085","display_name":"Randomization","level":3,"score":0.42459651827812195},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.413473904132843},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.379604309797287},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32025468349456787},{"id":"https://openalex.org/C168563851","wikidata":"https://www.wikidata.org/wiki/Q1436668","display_name":"Randomized controlled trial","level":2,"score":0.22715997695922852},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1261502504348755},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10534307360649109},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08230897784233093},{"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C141071460","wikidata":"https://www.wikidata.org/wiki/Q40821","display_name":"Surgery","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:10.1145/1993886.1993929","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1993886.1993929","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 36th international symposium on Symbolic and algebraic computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W138870135","https://openalex.org/W1422673929","https://openalex.org/W1489355995","https://openalex.org/W1502124338","https://openalex.org/W1599026900","https://openalex.org/W1828979180","https://openalex.org/W1968245619","https://openalex.org/W1974755392","https://openalex.org/W2000583785","https://openalex.org/W2017951318","https://openalex.org/W2020804487","https://openalex.org/W2031337945","https://openalex.org/W2036932727","https://openalex.org/W2041165203","https://openalex.org/W2052810429","https://openalex.org/W2080132708","https://openalex.org/W2086081089","https://openalex.org/W2088105597","https://openalex.org/W2089028133","https://openalex.org/W2170078634","https://openalex.org/W2289808822","https://openalex.org/W4210962357","https://openalex.org/W4211013128","https://openalex.org/W4211143631","https://openalex.org/W4289920060"],"related_works":["https://openalex.org/W2389462125","https://openalex.org/W2091997962","https://openalex.org/W151496359","https://openalex.org/W1969863203","https://openalex.org/W4220662591","https://openalex.org/W856465872","https://openalex.org/W1987843132","https://openalex.org/W4246602344","https://openalex.org/W1480644286","https://openalex.org/W2359223678"],"abstract_inverted_index":{"MBA":[0],"algorithm":[1],"inverts":[2],"a":[3,13,78],"structured":[4,70],"matrix":[5],"in":[6],"nearly":[7],"linear":[8],"arithmetic":[9],"time":[10],"but":[11],"requires":[12],"serious":[14],"restriction":[15,23],"on":[16,50,77],"the":[17,30,73],"input":[18],"class.":[19],"We":[20],"remove":[21],"this":[22],"by":[24],"means":[25],"of":[26,67,81,85],"randomization":[27],"and":[28,42,64,69,88],"extend":[29],"progress":[31,87],"to":[32],"some":[33],"fundamental":[34],"computations":[35,51],"with":[36,52],"polynomials,":[37],"e.g.,":[38],"computing":[39],"their":[40],"GCDs":[41],"AGCDs,":[43],"where":[44],"most":[45],"effective":[46],"known":[47],"algorithms":[48,60],"rely":[49],"matrices":[53],"having":[54],"Toeplitz-like":[55],"structure.":[56],"Furthermore,":[57],"our":[58,86],"randomized":[59],"fix":[61],"rank":[62],"deficiency":[63],"ill":[65],"conditioning":[66],"general":[68],"matrices.":[71],"At":[72],"end":[74],"we":[75],"comment":[76],"wide":[79],"range":[80],"other":[82],"natural":[83],"extensions":[84],"underlying":[89],"ideas.":[90]},"counts_by_year":[{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}