{“id”:“https://openalex.org/W1426742690“,”doi“:”https://doi.org/10.1137/140990280“,”title“:”深度-4公式计算迭代矩阵乘法的下限“,”display_name“:”计算迭代矩阵乘的深度-4公式的下限”,“publication_year”:2015,“publiation_date”:“2015-01-01”,“ids”:{“openalex”:“”https://openalex.org/W1426742690“,”doi“:”https://doi.org/10.1137/140990280“,”mag“:”1426742690“},”language“:”en“,”primary_location“:{”is_oa“:false,”landing_page_url“:”https://doi.org/10.1137/140990280“,”pdf_url“:null,”source“:{”id“:”https://openalex.org/S153560523“,”display_name“:”SIAM计算日志“,”issn_l“:”0097-5397“,”isn“:[”0097-50397“、”1095-7111“],”is_oa“:false,”is_in_doaj“:false,”host_organization“:”https://openalex.org/P4310320508“,”“host_organization_name”:“工业与应用数学学会”,“host_ordanization_lineage”:[“https://openalex.org/P4310320508“],”host_organization_lineage_names“:[”工业和应用数学学会“],“type”:“journal”},“license”:null,“licence_id”:null,“version”:nully,“is_accepted”:false,“is_published”:false},”type“:”article“,”type_crossref“:“jornal-article”,“indexed_in”:[”crossref“]any_repository_has_fulltext“:false},”作者身份“:[{”作者位置“:”第一个“,”作者“:{”id“:”https://openalex.org/A5004130370“,”display_name“:”Herv\u00e9 Fournier“,”orcid“:null},”institutions“:[],”countries“:[],”is_corresponding“:false,”raw_author_name“,”Herv\ u00e9-Fournier-“,”raw _affiliation_strings“:],”afliations“:【】},{”author_position“:”middle“,”author“:{”id“:”https://openalex.org/A5083072245“,”display_name“:”Nutan Limaye“,”orcid“:”https://orcid.org/0000-0002-0238-1674“},”机构“:[],”国家“:[[],”is_corresponding“:false,”raw_author_name“:”Nutan Limaye“,”raw _ afiliation_strings“:[],“从属关系”:[]},{“author_position”:“middle”,“author”:{“id”:“https://openalex.org/A5072821588“,”display_name“:”Guillaume Malod“,”orcid“:null},”institutions“:[],”countries“:[],”is_corresponding“:false,”raw_author_name“:”Guillaome Malod“,”raw _affiliation_strings“:],”affiliations“:[/]},{”author_position“:”last“,”author“:{”id“:”https://openalex.org/A5025305994“,”display_name“:”Srikanth Srinivasan“,”orcid“:”https://orcid.org/0000-0001-6491-124X“},”机构“:[],”国家“:[[],”is_corresponding“:false,”raw_author_name“:”Srikanth Srinivasan“,”raw _ afiliation_strings“:[],“从属关系”:[]}],“countries _ distinct_count”:0,“institutions _ disting_count“:0,”corresponding_author_ids“:[].,”correcponding_institution_ids 1.318,“has_fulltext”:假,“cited_by_count“:14,”cited_by_percentile_year“:{”min“:89,”max“:90},”biblio“:{”volume“:”44“,”issue“:”5“,”first_page“:”1173“,”last_page“:“1201”},“is_retracted”:false,“is_paratext”:false,“primary_topic”:{“id”:“https://openalex.org/T10720“,”display_name“:”组合优化与复杂性理论“,”score“:1.0,”subfield“:{”id“:”https://openalex.org/subfields/1703“,”display_name“:”计算理论与数学“},”字段“:{”id“:”https://openalex.org/fields/17“,”display_name“:”Computer Science“},”domain“:{”id“:”https://openalex.org/domains/3“,”display_name“:”物理科学“}},”主题“:[{”id“:”https://openalex.org/T10720“,”display_name“:”组合优化与复杂性理论“,”score“:1.0,”subfield“:{”id“:”https://openalex.org/subfields/1703“,”display_name“:”计算理论与数学“},”字段“:{”id“:”https://openalex.org/fields/17“,”display_name“:”Computer Science“},”domain“:{”id“:”https://openalex.org/domains/3“,”display_name“:”物理科学“}},{”id“:”https://openalex.org/T10237“,”“display_name”:“高级加密方案和协议”,“score”:0.9983,“subfield”:{“id”:“https://openalex.org/subfields/1702“,”display_name“:”人工智能“},”字段“:{”id“:”https://openalex.org/fields/17“,”display_name“:”Computer Science“},”domain“:{”id“:”https://openalex.org/domains/3“,”display_name“:”物理科学“}},{”id“:”https://openalex.org/T12072“,”“display_name”:“机器学习研究中的主动学习”,“score”:0.998,“subfield”:{“id”:“https://openalex.org/subfields/1702“,”display_name“:”人工智能“},”字段“:{”id“:”https://openalex.org/fields/17“,”display_name“:”Computer Science“},”domain“:{”id“:”https://openalex.org/domains/3“,”display_name“:”物理科学“}}],”关键词“:[{”id“:”https://openalex.org/keywords/matrix-乘法“,”display_name“:”矩阵乘法“,”score“:0.58126},{”id“:”https://openalex.org/keywords/privacy-保留计算“,”display_name“:”隐私保护计算“,”score“:0.502833}],”concepts“:[{”id“:”https://openalex.org/C33923547,“wikidata”:https://www.wikidata.org/wiki/Q395“,”display_name“:”数学“,”等级“:0,”分数“:0.74244434},{”id“:”https://openalex.org/C17349429,“wikidata”:https://www.wikidata.org/wiki/Q1049914“,”display_name“:”矩阵乘法“,”level“:3,”score“:0.71516937},{”id“:”https://openalex.org/C114614502,“wikidata”:https://www.wikidata.org/wiki/Q76592“,”display_name“:”组合数学“,”level“:1,”score“:0.6920692},{”id“:”https://openalex.org/C140479938,“wikidata”:https://www.wikidata.org/wiki/Q5254619(网址:https://www.wikidata.org/wiki/Q5254619)“,”display_name“:”迭代函数“,”level“:2,”score“:0.67475575},{”id“:”https://openalex.org/C84392682,“wikidata”:https://www.wikidata.org/wiki/Q1952404“,”display_name“:”多线性映射“,”level“:2,”score“:0.61379665},{”id“:”https://openalex.org/C2779557605,“wikidata”:https://www.wikidata.org/wiki/Q9890“,”display_name“:”Omega“,”level“:2,”score“:0.58378255},{”id“:”https://openalex.org/C9019067,“wikidata”:https://www.wikidata.org/wiki/Q43260“,”display_name“:”多项式“,”level“:2,”score“:0.52663094},{”id“:”https://openalex.org/C106487976,“wikidata”:https://www.wikidata.org/wiki/Q685816“,”display_name“:”Matrix(化学分析)“,”level“:2,”score“:0.51343334},{”id“:”https://openalex.org/C2775997480,“wikidata”:https://www.wikidata.org/wiki/Q586277“,”display_name“:”学位(音乐)“,”等级“:2,”分数“:0.4964233},{”id“:”https://openalex.org/C77553402,“wikidata”:https://www.wikidata.org/wiki/Q13222579“,”display_name“:”上下限“,”level“:2,”score“:0.49045488},{”id“:”https://openalex.org/C90673727,“wikidata”:https://www.wikidata.org/wiki/Q901718“,”display_name“:”乘积(数学)“,”level“:2,”score“:0.4798286},{”id“:”https://openalex.org/C2778049214,“wikidata”:https://www.wikidata.org/wiki/Q7512234“,”display_name“:”Sigma“,”level“:2,”score“:0.4438968},{”id“:”https://openalex.org/C118615104,“wikidata”:https://www.wikidata.org/wiki/Q121416“,”display_name“:”离散数学“,”level“:1,”score“:0.42815423},{”id“:”https://openalex.org/C121332964,“wikidata”:https://www.wikidata.org/wiki/Q413“,”display_name“:”物理“,”等级“:0,”分数“:0.13853234},{”id“:”https://openalex.org/C2524010,“wikidata”:https://www.wikidata.org/wiki/Q8087“,”display_name“:”Geometry“,”level“:1,”score“:0.13606599},{”id“:”https://openalex.org/C202444582,“wikidata”:https://www.wikidata.org/wiki/Q837863“,”display_name“:”纯数学“,”level“:1,”score“:0.113827884},{”id“:”https://openalex.org/C134306372,“wikidata”:https://www.wikidata.org/wiki/Q7754“,”display_name“:”数学分析“,”level“:1,”score“:0.098820865},{”id“:”https://openalex.org/C192562407,“wikidata”:https://www.wikidata.org/wiki/Q228736“,”display_name“:”材料科学“,”level“:0,”score“:0.0},{”id“:”https://openalex.org/C62520636,“wikidata”:https://www.wikidata.org/wiki/Q944“,”display_name“:”量子力学“,”level“:1,”score“:0.0},{”id“:”https://openalex.org/C159985019,“wikidata”:https://www.wikidata.org/wiki/Q181790“,”display_name“:”复合材料“,”level“:1,”score“:0.0},{”id“:”https://openalex.org/C84114770,“wikidata”:https://www.wikidata.org/wiki/Q46344“,”display_name“:”Quantum“,”level“:2,”score“:0.0},{”id“:”https://openalex.org/C24890656,“wikidata”:https://www.wikidata.org/wiki/Q82811“,”display_name“:”Acoustics“,”level“:1,”score“:0.0}],”mesh“:[],”locations_count“:1.”locations“:[{”is_oa“:false,”landing_page_url“:”https://doi.org/10.1137/140990280“,”pdf_url“:null,”source“:{”id“:”https://openalex.org/S153560523“,”display_name“:”SIAM计算日志“,”issn_l“:”0097-5397“,”isn“:[”0097-50397“、”1095-7111“],”is_oa“:false,”is_in_doaj“:false,”host_organization“:”https://openalex.org/P4310320508“,”“host_organization_name”:“工业与应用数学学会”,“host_ordanization_lineage”:[“https://openalex.org/P4310320508“],”host_organization_lineage_names“:[”工业与应用数学学会“],“type”:“journal”},“license”:null,“licence_id”:null',“version”:null,“is_accepted”:false,“is_published”:false}],“best_oa_location”:nul,“sustainable_development_goals”:[],“grants”:[],“datasets”:[/],“versions”:[]],“referenced_works_count”:8,“referrenced_works”:“[”https://openalex.org/W1988938797","https://openalex.org/W2016576580","https://openalex.org/W2026944800","https://openalex.org/W2060270693","https://openalex.org/W2087664562","https://openalex.org/W2110206454","https://openalex.org/W2171403864","https://openalex.org/W2172394696“],”related_works“:[”https://openalex.org/W4300097816","https://openalex.org/W4225414648","https://openalex.org/W3186548984","https://openalex.org/W3091839222","https://openalex.org/W3013407674","https://openalex.org/W3000087930","https://openalex.org/W2964040447","https://openalex.org/W2963154509","https://openalex.org/W2767623943","https://openalex.org/W2765850415“],”ngrams_url“:”https://api.openalex.org/works/W1426742690/ngrams“,”abstract_inverted_index“:{”We“:[0,9,58123],”study“:[1,60],”the“:[2,19,42,68,72,75136],”算术“:[3,16],”复杂性“:[4],”of“:[5,21,25,44,74,83107119138146152],”iterated“:[6],“矩阵”:[7],”乘法“:[8],”show“:[10124],”that“:[11,95125],”any“:%12,96126],”multillinear“:[13],“均质”:[14],“深度-4”:[15,55,65116],“公式“:[17118128],”计算“:[18129],”乘积“:[20],”$d$“:[22],”通用“:[23],”矩阵“:[24],”大小“:[26,32108],”$“:[2],”\\times“:[28],”n$,“:[29],”\\mathrm{即时消息}_{n,d}$,“:[30],”has“:[31131],”$n^{\\Omega(\\sqrt{d})}$“:[33],”as“:[34,36],”long“:[35],”$d“:[37,99],”=“:[38100],”n^{O(1)}$。“:[39],”This“:[40141],”improves“:[41],”result“:[43,822145],”Nisan“:[45],”and“:[46149],”Wigderson“:[47],”Comput.“:[48],”Complexity“:[49],”6“:[50],”(1997),“:[51],”pp.“:[52,92155],”217--234]“:[53],”for“:[54163],”set multilinear“:[56],”formulas。“:[57],”也“:[59111142],”$\\Sigma\\Pi^{[O(d/t)]}\\Sigma \\Pi^[t]}$“:[61117],”公式,“:[62],”其中“:[63157],”是“:[64],“公式”:[66],“with”:[67],“stated”:[69],“bounds”:[70],“on”:[71],“fan-ins”:[3],“$\\Pi$”:[76],“门。“:[77],“A”:[78],“recent”:[79],“depth”:[80],“reduction”:[81],“Tavenas”:[84],“[讲座”:[85],“注释”:[86],“in”:[87167],“计算”。“:[88],”科学。“:[89],”8087,“:[90],“2013,”:[91],“813--824]”:[93],“显示”:[94],“$n$-variate”:[97],“度”:[98],“n^{O(1)}$”:[101],“多项式”:[102166],“可计算”:[103],“by”:[104114],“a”:[105115144159],“电路”:[106],“$\\mathop{\\mathrm{poly}}}”(n)$“:[109],”can“:[110],”be“:[112],”computed“:[113],”top“:[1120132],”fan-in“:[121133],”$n^{O(d/t)}$。“:[122],”suke“:[127],”$\\mathrm{即时消息}_{n,d}$“:[130],”$n^{\\Omega({d/t})}$,“:[134],”证明“:[135],”最优性“:[137],”Tavenas“:[139],”结果。“:[140],”加强“:[143],”凯亚尔“:[147],”萨哈“:[148],”萨普塔里希“:[150],”[诉讼程序“:[151],”STOC“:[153],”2014“:[154],”146--153],“:[156],”给出“:[158],”类似“:[160],”更低“:[161],”绑定“:[162],”an“:[164],”显式“:[165],”VNP。“:[168]},”cited_by_api_url“:”https://api.openalex.org/works?filter=cites:W1426742690“,”“counts_by_year”:[{“年份”:2024,”“cited_by_count”:1},{“年度”:2022,”“cited_by_cunt”:2},}“年份“:2021,”updated_date“:”2024-06-21T12:51:08.547898“,”创建日期“:”2016-06-24“}