{"id":"https://openalex.org/W3150041682","doi":"https://doi.org/10.1109/tc.1973.5009182","title":"On Efficient Computation of Matrix Chain Products","display_name":"On Efficient Computation of Matrix Chain Products","publication_year":1973,"publication_date":"1973-09-01","ids":{"openalex":"https://openalex.org/W3150041682","doi":"https://doi.org/10.1109/tc.1973.5009182","mag":"3150041682"},"language":"en","primary_location":{"id":"doi:10.1109/tc.1973.5009182","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1973.5009182","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","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/A5110553447","display_name":"Sadashiva S. Godbole","orcid":null},"institutions":[{"id":"https://openalex.org/I21978226","display_name":"University of Lynchburg","ror":"https://ror.org/03grk0f38","country_code":"US","type":"education","lineage":["https://openalex.org/I21978226"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sadashiva S. Godbole","raw_affiliation_strings":["Babcock & Wilcox Company, Lynchburg Research Center, Lynchburg, Va. 24505"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Babcock & Wilcox Company, Lynchburg Research Center, Lynchburg, Va. 24505","institution_ids":["https://openalex.org/I21978226"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110553447"],"corresponding_institution_ids":["https://openalex.org/I21978226"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":78,"citation_normalized_percentile":{"value":0.50450789,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"C-22","issue":"9","first_page":"864","last_page":"866"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10715","display_name":"Distributed and Parallel Computing Systems","score":0.9922000169754028,"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"}},"topics":[{"id":"https://openalex.org/T10715","display_name":"Distributed and Parallel Computing Systems","score":0.9922000169754028,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9857000112533569,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9782999753952026,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.7724709510803223},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6792064905166626},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.6762915849685669},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6295350790023804},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6006916761398315},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5682096481323242},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5680126547813416},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5415288805961609},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5172927379608154},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.4737487733364105},{"id":"https://openalex.org/keywords/scalar-multiplication","display_name":"Scalar multiplication","score":0.4556770920753479},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4424193501472473},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38038352131843567},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3707699179649353},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.3333478569984436},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3287316560745239}],"concepts":[{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.7724709510803223},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6792064905166626},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.6762915849685669},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6295350790023804},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6006916761398315},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5682096481323242},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5680126547813416},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5415288805961609},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5172927379608154},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.4737487733364105},{"id":"https://openalex.org/C171182647","wikidata":"https://www.wikidata.org/wiki/Q126736","display_name":"Scalar multiplication","level":3,"score":0.4556770920753479},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4424193501472473},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38038352131843567},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3707699179649353},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.3333478569984436},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3287316560745239},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.1973.5009182","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1973.5009182","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7200000286102295,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W4252450337"],"related_works":["https://openalex.org/W2363723691","https://openalex.org/W4231584466","https://openalex.org/W2765331211","https://openalex.org/W1602189784","https://openalex.org/W2296442452","https://openalex.org/W4236829276","https://openalex.org/W3194333422","https://openalex.org/W3094950822","https://openalex.org/W2050885298","https://openalex.org/W3134740226"],"abstract_inverted_index":{"It":[0],"is":[1,30,34,50],"pointed":[2],"out":[3,67],"that":[4,41,92],"the":[5,20,24,38,43,55,68,73,82,96],"number":[6,44],"of":[7,27,45,98,108,115],"scalar":[8,46],"multiplications":[9],"(additions)":[10],"required":[11],"to":[12,36,59,65,72,80],"evaluate":[13],"a":[14],"matrix":[15,28,116],"chain":[16,69,106,119],"product":[17,70],"depends":[18],"on":[19,54],"sequence":[21,40],"in":[22,86,90,112],"which":[23],"associative":[25],"law":[26],"multiplication":[29],"applied.":[31],"An":[32],"algorithm":[33,62,100],"developed":[35],"find":[37],"optimum":[39,74],"minimizes":[42],"multiplications.":[47],"A":[48],"program":[49],"written":[51],"for":[52,105],"use":[53,97],"CDC":[56],"6600":[57],"computer":[58],"implement":[60],"this":[61,99],"and":[63,88,111],"also":[64],"carry":[66],"according":[71],"sequence.":[75],"Several":[76],"examples":[77],"are":[78],"included":[79],"illustrate":[81],"algorithm.":[83],"The":[84],"saving":[85],"computation":[87],"improvement":[89],"accuracy":[91],"can":[93,101],"result":[94],"from":[95],"be":[102],"quite":[103],"significant":[104],"products":[107],"large":[109],"arrays":[110],"iterative":[113],"solutions":[114],"equations":[117],"involving":[118],"products.":[120]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}