{"id":"https://openalex.org/W2505206507","doi":"https://doi.org/10.1137/1.9781611973082.40","title":"Approximating Matrix p-norms","display_name":"Approximating Matrix p-norms","publication_year":2011,"publication_date":"2011-01-23","ids":{"openalex":"https://openalex.org/W2505206507","doi":"https://doi.org/10.1137/1.9781611973082.40","mag":"2505206507"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/1.9781611973082.40","pdf_url":null,"source":null,"license":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"proceedings-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1001.2613","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014414126","display_name":"Aditya Bhaskara","orcid":"https://orcid.org/0000-0001-5505-3140"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aditya Bhaskara","raw_affiliation_string":"","raw_affiliation_strings":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5081431077","display_name":"Aravindan Vijayaraghavan","orcid":"https://orcid.org/0000-0001-9734-3779"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aravindan Vijayaraghavan","raw_affiliation_string":"","raw_affiliation_strings":[]}],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"has_fulltext":false,"cited_by_count":8,"cited_by_percentile_year":{"min":86,"max":87},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Combinatorial Optimization and Complexity Theory","score":0.999,"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/T10720","display_name":"Combinatorial Optimization and Complexity Theory","score":0.999,"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/T12288","display_name":"Distributed Coordination in Online Robotics Research","score":0.9988,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10374","display_name":"Graph Theory and Algorithms","score":0.9964,"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":[{"keyword":"matrix","score":0.3758}],"concepts":[{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6824539},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.603269},{"id":"https://openalex.org/C162443888","wikidata":"https://www.wikidata.org/wiki/Q1426504","display_name":"Power iteration","level":3,"score":0.5716872},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.57117385},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5376434},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5092226},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4720821},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.45105848},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44634813},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44291037},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38307726},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.26900876},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26021922},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/1.9781611973082.40","pdf_url":null,"source":null,"license":null,"version":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1001.2613","pdf_url":"https://arxiv.org/pdf/1001.2613","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1001.2613","pdf_url":"https://arxiv.org/pdf/1001.2613","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1242461565","https://openalex.org/W2141849896","https://openalex.org/W3023273287","https://openalex.org/W4309047765","https://openalex.org/W2363016166","https://openalex.org/W4293861650","https://openalex.org/W2161448262","https://openalex.org/W1606970495","https://openalex.org/W2949544809","https://openalex.org/W2231174965"],"ngrams_url":"https://api.openalex.org/works/W2505206507/ngrams","abstract_inverted_index":{"Previous":[0,321],"chapter":[1,3,322,324],"Next":[2,323],"Full":[4],"AccessProceedings":[5],"Proceedings":[6],"of":[7,40,47,73,77,91,98,123,129,146,176,187,193,211,279],"the":[8,38,42,74,104,121,124,141,191,201,233,244,252,277,305],"2011":[9],"Annual":[10],"ACM-SIAM":[11],"Symposium":[12],"on":[13,163,216,243],"Discrete":[14],"Algorithms":[15],"(SODA)Approximating":[16],"Matrix":[17],"p-normsAditya":[18],"Bhaskara":[19,23],"and":[20,24,68,111,213,268],"Aravindan":[21,25],"VijayaraghavanAditya":[22],"Vijayaraghavanpp.497":[26],"-":[27],"511Chapter":[28],"DOI:https://doi.org/10.1137/1.9781611973082.40PDFBibTexSections":[29],"ToolsAdd":[30],"to":[31,83,95,190,256,258,310],"favoritesExport":[32],"CitationTrack":[33],"CitationsEmail":[34],"SectionsAboutAbstract":[35],"We":[36,182],"consider":[37],"problem":[39,106,125,192,253,306],"computing":[41,78,140,180],"q":[43,56,86,112,142,152,267,271,281,285],"\u2192":[44,143],"p":[45,84,108,144,154,229,265,269,283],"norm":[46,145],"a":[48,64,70,96,164,195,207,311],"matrix":[49],"A,":[50],"which":[51,169],"is":[52,61,69,118,135,161,254],"defined":[53],"for":[54,126,139,179,197,228,262,315],"p,":[55,130,280],"\u2265":[57,153,155],"1,":[58],"as":[59,103,173,247],"This":[60,204],"in":[62,200],"general":[63],"non-convex":[65],"optimization":[66],"problem,":[67],"natural":[71,165],"generalization":[72],"well-studied":[75],"question":[76],"singular":[79],"values":[80,128],"(this":[81],"corresponds":[82],"=":[85,87,109,113,230],"2).":[88,231],"Different":[89],"settings":[90],"parameters":[92],"give":[93],"rise":[94],"variety":[97],"known":[99],"interesting":[100],"problems":[101],"(such":[102,246],"Grothendieck":[105],"when":[107,151,236],"1":[110],"\u221e).":[114],"However,":[115],"very":[116],"little":[117],"understood":[119],"about":[120],"approximability":[122],"different":[127],"q.":[131],"Our":[132],"first":[133],"result":[134,210],"an":[136,174,185],"efficient":[137],"algorithm":[138,158],"matrices":[147],"with":[148,282],"non-negative":[149],"entries,":[150],"1.":[156],"The":[157],"we":[159,237,249],"analyze":[160],"based":[162],"fixed":[166],"point":[167],"iteration,":[168],"can":[170],"be":[171,308],"seen":[172],"analog":[175],"power":[177],"iteration":[178],"eigenvalues.":[181],"then":[183],"present":[184],"application":[186],"our":[188,296],"techniques":[189,297],"constructing":[194],"scheme":[196],"oblivious":[198,220],"routing":[199,221],"\u2113p":[202],"norm.":[203],"makes":[205],"constructive":[206,226],"recent":[208],"existential":[209],"Englert":[212],"R\u00e4cke":[214],"[ER09]":[215],"O(log":[217],"n)":[218],"competitive":[219],"schemes":[222],"(which":[223],"they":[224],"make":[225],"only":[227],"On":[232],"other":[234],"hand,":[235],"do":[238],"not":[239,291],"have":[240],"any":[241,259,316],"restrictions":[242],"entries":[245],"non-negativity),":[248],"prove":[250],"that":[251,300],"NP-hard":[255],"approximate":[257],"constant":[260,287,317],"factor,":[261],"2":[263,273],"<":[264,272],"\u2264":[266,270,284],"(these":[274],"are":[275,290],"precisely":[276],"ranges":[278],"where":[286],"factor":[288,312],"approximations":[289],"known).":[292],"In":[293],"this":[294],"range,":[295],"also":[298],"show":[299],"if":[301],"NP":[302],"\u2209":[303],"DTIME(npolylog(n)),":[304],"cannot":[307],"approximated":[309],"2(log":[313],"n)1\u2013\u03b5,":[314],"\u03b5":[318],">":[319],"0.":[320],"RelatedDetails":[325],"Published:2011ISBN:978-0-89871-993-2eISBN:978-1-61197-308-2":[326],"https://doi.org/10.1137/1.9781611973082Book":[327],"Series":[328],"Name:ProceedingsBook":[329],"Code:PR138Book":[330],"Pages:xviii-1788":[331]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2505206507","counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2024-03-26T06:11:35.397623","created_date":"2016-08-23"}