{"id":"https://openalex.org/W2005277542","doi":"https://doi.org/10.1145/2442829.2442832","title":"Asymptotic spectrum and matrix multiplication","display_name":"Asymptotic spectrum and matrix multiplication","publication_year":2012,"publication_date":"2012-07-22","ids":{"openalex":"https://openalex.org/W2005277542","doi":"https://doi.org/10.1145/2442829.2442832","mag":"2005277542"},"language":"en","primary_location":{"id":"doi:10.1145/2442829.2442832","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2442829.2442832","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"conference-paper","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/A5007475314","display_name":"Volker Strassen","orcid":null},"institutions":[{"id":"https://openalex.org/I189712700","display_name":"University of Konstanz","ror":"https://ror.org/0546hnb39","country_code":"DE","type":"education","lineage":["https://openalex.org/I189712700"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Volker Strassen","raw_affiliation_strings":["Universit\u00e4t Konstanz"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Konstanz","institution_ids":["https://openalex.org/I189712700"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007475314"],"corresponding_institution_ids":["https://openalex.org/I189712700"],"apc_list":null,"apc_paid":null,"fwci":0.2602,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.46793968,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"6","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9969000220298767,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/multiplication","display_name":"Multiplication (music)","score":0.7069813013076782},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.6559778451919556},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6224855184555054},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.5432987213134766},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.5361793637275696},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.5141932964324951},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5050914883613586},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.48398590087890625},{"id":"https://openalex.org/keywords/algebraic-operation","display_name":"Algebraic operation","score":0.47648710012435913},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.45296549797058105},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4479597508907318},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.43545228242874146},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.43229323625564575},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4292064607143402},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.42071813344955444},{"id":"https://openalex.org/keywords/bilinear-map","display_name":"Bilinear map","score":0.41280660033226013},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3002592623233795},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29837894439697266},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13352757692337036},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09598460793495178}],"concepts":[{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.7069813013076782},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.6559778451919556},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6224855184555054},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5432987213134766},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5361793637275696},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.5141932964324951},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5050914883613586},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.48398590087890625},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.47648710012435913},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.45296549797058105},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4479597508907318},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.43545228242874146},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.43229323625564575},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4292064607143402},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.42071813344955444},{"id":"https://openalex.org/C142685569","wikidata":"https://www.wikidata.org/wiki/Q1086961","display_name":"Bilinear map","level":3,"score":0.41280660033226013},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3002592623233795},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29837894439697266},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13352757692337036},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09598460793495178},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2442829.2442832","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2442829.2442832","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2946208069","https://openalex.org/W4242229754","https://openalex.org/W1994004144","https://openalex.org/W1963546854","https://openalex.org/W4287102253","https://openalex.org/W3028820650","https://openalex.org/W3177913317","https://openalex.org/W2060343138","https://openalex.org/W2783191749","https://openalex.org/W2031905258"],"abstract_inverted_index":{"The":[0,53],"minimal":[1],"number":[2],"of":[3,10,36,44,50,67],"arithmetic":[4],"operations":[5],"sufficient":[6],"to":[7,24,29,55],"multiply":[8],"matrices":[9],"order":[11],"m":[12,27],"by":[13],"an":[14],"algebraic":[15],"circuit":[16],"has":[17,58],"the":[18,34,42,60,65],"form":[19],"m\u03c9+o(1),":[20],"where":[21],"o(1)":[22],"goes":[23],"zero":[25],"when":[26],"tends":[28],"infinity.":[30],"\u03c9":[31,57],"is":[32],"called":[33],"exponent":[35],"matrix":[37],"multiplication.":[38],"Asymptotically,":[39],"it":[40],"controls":[41],"complexity":[43,66],"almost":[45],"all":[46],"significant":[47],"computational":[48],"tasks":[49],"linear":[51],"algebra.":[52],"desire":[54],"determine":[56],"been":[59],"main":[61],"motivation":[62],"for":[63],"investigating":[64],"bilinear":[68],"maps":[69],"in":[70],"general.":[71]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
