{"id":"https://openalex.org/W1883653182","doi":"https://doi.org/10.1137/100788884","title":"Improved Bounds on Restricted Isometry Constants for Gaussian Matrices","display_name":"Improved Bounds on Restricted Isometry Constants for Gaussian Matrices","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1883653182","doi":"https://doi.org/10.1137/100788884","mag":"1883653182"},"language":"en","primary_location":{"id":"doi:10.1137/100788884","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100788884","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":true,"oa_status":"green","oa_url":"https://www.research.ed.ac.uk/en/publications/00770082-536b-437d-86c4-3d34dbbef6d3","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008341060","display_name":"Bubacarr Bah","orcid":"https://orcid.org/0000-0003-3318-6668"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bubacarr Bah","raw_affiliation_strings":["b.bah@sms.ed.ac.uk and jared.tanner@ed.ac.uk#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"b.bah@sms.ed.ac.uk and jared.tanner@ed.ac.uk#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059562923","display_name":"Jared Tanner","orcid":"https://orcid.org/0000-0002-5561-9949"},"institutions":[{"id":"https://openalex.org/I4210117017","display_name":"Maxwell Institute for Mathematical Sciences","ror":"https://ror.org/02tsqtg57","country_code":"GB","type":"facility","lineage":["https://openalex.org/I32062511","https://openalex.org/I4210117017","https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jared Tanner","raw_affiliation_strings":["Univ Edinburgh, Maxwell Inst"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ Edinburgh, Maxwell Inst","institution_ids":["https://openalex.org/I4210117017"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.4078,"has_fulltext":false,"cited_by_count":76,"citation_normalized_percentile":{"value":0.97033837,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"31","issue":"5","first_page":"2882","last_page":"2898"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9998999834060669,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991000294685364,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9976999759674072,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8803382515907288},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7505851984024048},{"id":"https://openalex.org/keywords/isometry","display_name":"Isometry (Riemannian geometry)","score":0.6961477398872375},{"id":"https://openalex.org/keywords/restricted-isometry-property","display_name":"Restricted isometry property","score":0.6076329350471497},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.589873731136322},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5748714804649353},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5513982176780701},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5349112153053284},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.51357102394104},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.5106211304664612},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.494627445936203},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.473977267742157},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32881098985671997},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18865758180618286},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1707722544670105},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.12041476368904114},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08499300479888916},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.08097663521766663}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8803382515907288},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7505851984024048},{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.6961477398872375},{"id":"https://openalex.org/C17902559","wikidata":"https://www.wikidata.org/wiki/Q17099734","display_name":"Restricted isometry property","level":3,"score":0.6076329350471497},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.589873731136322},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5748714804649353},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5513982176780701},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5349112153053284},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.51357102394104},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.5106211304664612},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.494627445936203},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.473977267742157},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32881098985671997},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18865758180618286},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1707722544670105},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.12041476368904114},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08499300479888916},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.08097663521766663},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer 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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/100788884","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100788884","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"},{"id":"pmh:oai:pure.ed.ac.uk:openaire/00770082-536b-437d-86c4-3d34dbbef6d3","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/00770082-536b-437d-86c4-3d34dbbef6d3","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bah, B & Tanner, J 2010, 'IMPROVED BOUNDS ON RESTRICTED ISOMETRY CONSTANTS FOR GAUSSIAN MATRICES', SIAM Journal on Matrix Analysis and Applications, vol. 31, no. 5, pp. 2882-2898. https://doi.org/10.1137/100788884","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.ed.ac.uk:ec_fundedresources/00770082-536b-437d-86c4-3d34dbbef6d3","is_oa":false,"landing_page_url":"https://hdl.handle.net/20.500.11820/00770082-536b-437d-86c4-3d34dbbef6d3","pdf_url":null,"source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:pure.ed.ac.uk:openaire/00770082-536b-437d-86c4-3d34dbbef6d3","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/00770082-536b-437d-86c4-3d34dbbef6d3","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bah, B & Tanner, J 2010, 'IMPROVED BOUNDS ON RESTRICTED ISOMETRY CONSTANTS FOR GAUSSIAN MATRICES', SIAM Journal on Matrix Analysis and Applications, vol. 31, no. 5, pp. 2882-2898. https://doi.org/10.1137/100788884","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1573820523","https://openalex.org/W1974755392","https://openalex.org/W2012961725","https://openalex.org/W2015418199","https://openalex.org/W2018429487","https://openalex.org/W2026653661","https://openalex.org/W2028781966","https://openalex.org/W2039343706","https://openalex.org/W2046351805","https://openalex.org/W2057503509","https://openalex.org/W2066086960","https://openalex.org/W2094503020","https://openalex.org/W2097417531","https://openalex.org/W2129131372","https://openalex.org/W2141097208","https://openalex.org/W2144629557","https://openalex.org/W2145096794","https://openalex.org/W2150386037","https://openalex.org/W2160979406","https://openalex.org/W2289917018","https://openalex.org/W2296616510","https://openalex.org/W2556237558","https://openalex.org/W2963322354","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W4237430004","https://openalex.org/W2025666718","https://openalex.org/W2151106956","https://openalex.org/W2951968883","https://openalex.org/W3104861007","https://openalex.org/W2975405901","https://openalex.org/W2122469757","https://openalex.org/W2145432339","https://openalex.org/W2741884985","https://openalex.org/W2164717810"],"abstract_inverted_index":{"The":[0],"restricted":[1],"isometry":[2,14],"constant":[3],"(RIC)":[4],"of":[5,18,37,41,55,62,65,78,102,141,161],"a":[6,38,158],"matrix":[7,39],"A":[8,19,40],"measures":[9],"how":[10],"close":[11],"to":[12,87,148],"an":[13],"is":[15,81,119],"the":[16,28,32,46,49,56,79,108,113,121,126,138],"action":[17],"on":[20,112,125,137],"vectors":[21],"with":[22,150],"few":[23],"nonzero":[24],"entries,":[25],"measured":[26],"in":[27,99],"$\\ell^2$":[29],"norm.":[30],"Specifically,":[31],"upper":[33],"and":[34,48,58,144],"lower":[35],"RICs":[36],"size":[42],"$n\\times":[43],"N$":[44],"are":[45,135],"maximum":[47],"minimum":[50],"deviation":[51],"from":[52,75],"unity":[53],"(one)":[54],"largest":[57],"smallest,":[59],"respectively,":[60],"square":[61],"singular":[63],"values":[64],"all":[66],"${N\\choose":[67],"k}$":[68],"matrices":[69,85,94],"formed":[70],"by":[71,153],"taking":[72],"k":[73],"columns":[74],"A.":[76],"Calculation":[77],"RIC":[80,98,114,127],"intractable":[82],"for":[83,115,128],"most":[84],"due":[86],"its":[88],"combinatorial":[89],"nature;":[90],"however,":[91],"many":[92],"random":[93],"typically":[95],"have":[96],"bounded":[97],"some":[100],"range":[101],"problem":[103],"sizes":[104],"$(k,n,N)$.":[105],"We":[106],"provide":[107],"best":[109],"known":[110,123],"bound":[111,124],"Gaussian":[116],"matrices,":[117],"which":[118],"also":[120],"smallest":[122],"any":[129],"large":[130],"rectangular":[131],"matrix.":[132],"Our":[133],"results":[134],"built":[136],"prior":[139],"bounds":[140],"Blanchard,":[142],"Cartis,":[143],"Tanner":[145],"[SIAM":[146],"Rev.,":[147],"appear],":[149],"improvements":[151],"achieved":[152],"grouping":[154],"submatrices":[155],"that":[156],"share":[157],"substantial":[159],"number":[160],"columns.":[162]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":8}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
