{"id":"https://openalex.org/W2181094752","doi":"https://doi.org/10.1145/2809812","title":"Work-Efficient Matrix Inversion in Polylogarithmic Time","display_name":"Work-Efficient Matrix Inversion in Polylogarithmic Time","publication_year":2015,"publication_date":"2015-09-08","ids":{"openalex":"https://openalex.org/W2181094752","doi":"https://doi.org/10.1145/2809812","mag":"2181094752"},"language":"en","primary_location":{"id":"doi:10.1145/2809812","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2809812","pdf_url":null,"source":{"id":"https://openalex.org/S2483380313","display_name":"ACM Transactions on Parallel Computing","issn_l":"2329-4949","issn":["2329-4949","2329-4957"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Parallel Computing","raw_type":"journal-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/A5082922326","display_name":"Peter Sanders","orcid":"https://orcid.org/0000-0003-3330-9349"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Peter Sanders","raw_affiliation_strings":["Institute for Theoretical Informatics, Karlsruhe Institute of Technology, Karlsruhe, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Informatics, Karlsruhe Institute of Technology, Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074144511","display_name":"Jochen Speck","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jochen Speck","raw_affiliation_strings":["Institute for Theoretical Informatics, Karlsruhe Institute of Technology, Karlsruhe, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Informatics, Karlsruhe Institute of Technology, Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070996239","display_name":"Raoul Steffen","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Raoul Steffen","raw_affiliation_strings":["Institute for Theoretical Informatics, Karlsruhe Institute of Technology, Karlsruhe, Germany"],"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Informatics, Karlsruhe Institute of Technology, Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5082922326"],"corresponding_institution_ids":["https://openalex.org/I102335020"],"apc_list":null,"apc_paid":null,"fwci":0.323,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60610976,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2","issue":"3","first_page":"1","last_page":"29"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987000226974487,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9973000288009644,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/strassen-algorithm","display_name":"Strassen algorithm","score":0.9507790207862854},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.6886637210845947},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.6451600790023804},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.605083703994751},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5596780776977539},{"id":"https://openalex.org/keywords/massively-parallel","display_name":"Massively parallel","score":0.49200913310050964},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4800875782966614},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4508424401283264},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34856176376342773},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.32627394795417786}],"concepts":[{"id":"https://openalex.org/C39096654","wikidata":"https://www.wikidata.org/wiki/Q728507","display_name":"Strassen algorithm","level":4,"score":0.9507790207862854},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.6886637210845947},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.6451600790023804},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.605083703994751},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5596780776977539},{"id":"https://openalex.org/C190475519","wikidata":"https://www.wikidata.org/wiki/Q544384","display_name":"Massively parallel","level":2,"score":0.49200913310050964},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4800875782966614},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4508424401283264},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34856176376342773},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.32627394795417786},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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:10.1145/2809812","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2809812","pdf_url":null,"source":{"id":"https://openalex.org/S2483380313","display_name":"ACM Transactions on Parallel Computing","issn_l":"2329-4949","issn":["2329-4949","2329-4957"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Parallel Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309370","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W201315547","https://openalex.org/W1965419971","https://openalex.org/W1978444682","https://openalex.org/W1979036815","https://openalex.org/W2018345399","https://openalex.org/W2029342163","https://openalex.org/W2032839380","https://openalex.org/W2033895300","https://openalex.org/W2035080386","https://openalex.org/W2035476608","https://openalex.org/W2038073775","https://openalex.org/W2064744742","https://openalex.org/W2091101062","https://openalex.org/W2102291960","https://openalex.org/W2110873104","https://openalex.org/W2113097540","https://openalex.org/W2120762604","https://openalex.org/W2124480634","https://openalex.org/W2153439050","https://openalex.org/W2154632851","https://openalex.org/W2160054705","https://openalex.org/W2187691968","https://openalex.org/W2480515730","https://openalex.org/W3099472489","https://openalex.org/W3103849684","https://openalex.org/W4234740575","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1974407206","https://openalex.org/W2004916460","https://openalex.org/W2962985479","https://openalex.org/W2020777648","https://openalex.org/W1523285705","https://openalex.org/W2772956802","https://openalex.org/W2056120647","https://openalex.org/W1829171354","https://openalex.org/W2069906535","https://openalex.org/W4387712010"],"abstract_inverted_index":{"We":[0,66],"present":[1],"an":[2,17,57],"algorithm":[3,34,71,84],"for":[4,80],"inversion":[5,36],"of":[6,16,20,27,63],"symmetric":[7],"positive":[8],"definite":[9],"matrices":[10],"that":[11,69,85],"combines":[12],"the":[13,24,47,52,70],"practical":[14],"requirement":[15],"optimal":[18],"number":[19],"arithmetic":[21],"operations":[22],"and":[23],"theoretical":[25],"goal":[26],"a":[28,78,81],"polylogarithmic":[29],"critical":[30,48],"path":[31,49],"length.":[32],"The":[33],"reduces":[35],"to":[37,56,87],"matrix":[38],"multiplication.":[39],"It":[40],"uses":[41],"Strassen\u2019s":[42],"recursion":[43,53],"scheme,":[44],"but":[45],"on":[46,91],"it":[50],"breaks":[51],"early,":[54],"switching":[55],"asymptotically":[58],"inefficient":[59],"yet":[60],"fast":[61],"use":[62],"Newton\u2019s":[64],"method.":[65],"also":[67],"show":[68],"is":[72],"numerically":[73],"stable.":[74],"Overall,":[75],"we":[76],"get":[77],"candidate":[79],"massively":[82],"parallel":[83],"scales":[86],"exascale":[88],"systems":[89],"even":[90],"relatively":[92],"small":[93],"inputs.":[94]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
