{"id":"https://openalex.org/W2007768252","doi":"https://doi.org/10.1137/s0895479896297744","title":"Locality of Reference in LU Decomposition with Partial Pivoting","display_name":"Locality of Reference in LU Decomposition with Partial Pivoting","publication_year":1997,"publication_date":"1997-10-01","ids":{"openalex":"https://openalex.org/W2007768252","doi":"https://doi.org/10.1137/s0895479896297744","mag":"2007768252"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479896297744","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479896297744","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056808449","display_name":"Sivan Toledo","orcid":"https://orcid.org/0000-0002-9524-7115"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sivan Toledo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5056808449"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.8255,"has_fulltext":false,"cited_by_count":160,"citation_normalized_percentile":{"value":0.95973496,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"18","issue":"4","first_page":"1065","last_page":"1081"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9983999729156494,"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":0.9983999729156494,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9966999888420105,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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":0.7942978143692017},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6940270662307739},{"id":"https://openalex.org/keywords/lu-decomposition","display_name":"LU decomposition","score":0.6760455369949341},{"id":"https://openalex.org/keywords/locality","display_name":"Locality","score":0.6354411840438843},{"id":"https://openalex.org/keywords/freivalds-algorithm","display_name":"Freivalds' algorithm","score":0.5281964540481567},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.516871452331543},{"id":"https://openalex.org/keywords/cache-oblivious-algorithm","display_name":"Cache-oblivious algorithm","score":0.49921274185180664},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49066102504730225},{"id":"https://openalex.org/keywords/cache","display_name":"Cache","score":0.4644363820552826},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44639289379119873},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4429762661457062},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.43871426582336426},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.3350125551223755},{"id":"https://openalex.org/keywords/cache-algorithms","display_name":"Cache algorithms","score":0.2752189636230469},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.2611566185951233},{"id":"https://openalex.org/keywords/cpu-cache","display_name":"CPU cache","score":0.19094038009643555},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.14991417527198792}],"concepts":[{"id":"https://openalex.org/C39096654","wikidata":"https://www.wikidata.org/wiki/Q728507","display_name":"Strassen algorithm","level":4,"score":0.7942978143692017},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6940270662307739},{"id":"https://openalex.org/C123213974","wikidata":"https://www.wikidata.org/wiki/Q833089","display_name":"LU decomposition","level":4,"score":0.6760455369949341},{"id":"https://openalex.org/C2779808786","wikidata":"https://www.wikidata.org/wiki/Q6664603","display_name":"Locality","level":2,"score":0.6354411840438843},{"id":"https://openalex.org/C38506071","wikidata":"https://www.wikidata.org/wiki/Q6522941","display_name":"Freivalds' algorithm","level":5,"score":0.5281964540481567},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.516871452331543},{"id":"https://openalex.org/C59687516","wikidata":"https://www.wikidata.org/wiki/Q5015938","display_name":"Cache-oblivious algorithm","level":5,"score":0.49921274185180664},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49066102504730225},{"id":"https://openalex.org/C115537543","wikidata":"https://www.wikidata.org/wiki/Q165596","display_name":"Cache","level":2,"score":0.4644363820552826},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44639289379119873},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4429762661457062},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.43871426582336426},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.3350125551223755},{"id":"https://openalex.org/C38556500","wikidata":"https://www.wikidata.org/wiki/Q13404475","display_name":"Cache algorithms","level":4,"score":0.2752189636230469},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.2611566185951233},{"id":"https://openalex.org/C189783530","wikidata":"https://www.wikidata.org/wiki/Q352090","display_name":"CPU cache","level":3,"score":0.19094038009643555},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.14991417527198792},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C173870130","wikidata":"https://www.wikidata.org/wiki/Q8548","display_name":"Dijkstra's algorithm","level":4,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895479896297744","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479896297744","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:CiteSeerX.psu:10.1.1.32.4811","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.4811","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.tau.ac.il/~stoledo/pubs/029774.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1972907356","https://openalex.org/W2004711550","https://openalex.org/W2006097867","https://openalex.org/W2007768252","https://openalex.org/W2035476608","https://openalex.org/W2037313761","https://openalex.org/W2040832766","https://openalex.org/W2061055167","https://openalex.org/W2076278082","https://openalex.org/W4403553343"],"related_works":["https://openalex.org/W4288024409","https://openalex.org/W2986341480","https://openalex.org/W1972907356","https://openalex.org/W1974407206","https://openalex.org/W3204033665","https://openalex.org/W2041189380","https://openalex.org/W4289143641","https://openalex.org/W4301181185","https://openalex.org/W1978106295","https://openalex.org/W2901988615"],"abstract_inverted_index":{"This":[0],"paper":[1,31],"presents":[2],"a":[3,24,47,69,130],"new":[4,14,39,66,115,127,142],"partitioned":[5,19,52],"algorithm":[6,40,53,67,116,120,128,134,143,151],"for":[7,54,107],"LU":[8,55],"decomposition":[9,56],"with":[10],"partial":[11],"pivoting.":[12],"The":[13,30,61,99],"algorithm,":[15,20,82],"called":[16,57],"the":[17,28,33,38,42,58,65,80,86,89,94,103,108,114,118,126,141],"recursively":[18],"is":[21,85,93],"based":[22],"on":[23,135],"recursive":[25],"partitioning":[26],"of":[27,35,44,71,88,96,125],"matrix.":[29],"analyzes":[32],"locality":[34,43],"reference":[36,45],"in":[37,46],"and":[41,49,91,117,153],"known":[48],"widely":[50],"used":[51],"right-looking":[59,81,109,119,133],"algorithm.":[60,110,161],"analysis":[62,100],"reveals":[63],"that":[64,122,140,154],"performs":[68,144],"factor":[70],"$\\Theta(\\sqrt{M/n})$":[72],"fewer":[73,145],"I/O":[74],"operations":[75],"(or":[76],"cache":[77,146],"misses)":[78],"than":[79,148],"where":[83],"n":[84],"order":[87],"matrix":[90],"M":[92],"size":[95,106],"primary":[97],"memory.":[98],"also":[101],"determines":[102],"optimal":[104],"block":[105],"Experimental":[111],"comparisons":[112],"between":[113],"show":[121],"an":[123],"implementation":[124],"outperforms":[129],"similarly":[131],"coded":[132],"six":[136],"different":[137],"RISC":[138],"architectures,":[139],"misses":[147],"any":[149],"other":[150],"tested,":[152],"it":[155],"benefits":[156],"more":[157],"from":[158],"Strassen's":[159],"matrix-multiplication":[160]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}