{"id":"https://openalex.org/W1991173951","doi":"https://doi.org/10.1137/13093426x","title":"Sparse Matrix-Matrix Products Executed Through Coloring","display_name":"Sparse Matrix-Matrix Products Executed Through Coloring","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1991173951","doi":"https://doi.org/10.1137/13093426x","mag":"1991173951"},"language":"en","primary_location":{"id":"doi:10.1137/13093426x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/13093426x","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/A5037355311","display_name":"Michael McCourt","orcid":"https://orcid.org/0000-0003-4531-7733"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael McCourt","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012464169","display_name":"Barry Smith","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Barry Smith","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5060364014","display_name":"Hong Zhang","orcid":"https://orcid.org/0000-0003-3480-0244"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hong Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5291,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.92896604,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"36","issue":"1","first_page":"90","last_page":"109"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9968000054359436,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9968000054359436,"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/T10715","display_name":"Distributed and Parallel Computing Systems","score":0.9897000193595886,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9886000156402588,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.7948874235153198},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6326053738594055},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.6041507720947266},{"id":"https://openalex.org/keywords/matrix-free-methods","display_name":"Matrix-free methods","score":0.5969710946083069},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5481054782867432},{"id":"https://openalex.org/keywords/nonnegative-matrix","display_name":"Nonnegative matrix","score":0.448814332485199},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.4422149360179901},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.4286416172981262},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.42478758096694946},{"id":"https://openalex.org/keywords/band-matrix","display_name":"Band matrix","score":0.4108322262763977},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39975398778915405},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3532658815383911},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.3479883670806885},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3335108757019043},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3202609419822693},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.31174230575561523},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10334131121635437}],"concepts":[{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.7948874235153198},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6326053738594055},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.6041507720947266},{"id":"https://openalex.org/C54219892","wikidata":"https://www.wikidata.org/wiki/Q4080929","display_name":"Matrix-free methods","level":4,"score":0.5969710946083069},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5481054782867432},{"id":"https://openalex.org/C139018669","wikidata":"https://www.wikidata.org/wiki/Q6961560","display_name":"Nonnegative matrix","level":4,"score":0.448814332485199},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.4422149360179901},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.4286416172981262},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.42478758096694946},{"id":"https://openalex.org/C33343441","wikidata":"https://www.wikidata.org/wiki/Q806350","display_name":"Band matrix","level":5,"score":0.4108322262763977},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39975398778915405},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3532658815383911},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.3479883670806885},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3335108757019043},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3202609419822693},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.31174230575561523},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10334131121635437},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/13093426x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/13093426x","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W19451620","https://openalex.org/W90568776","https://openalex.org/W149461665","https://openalex.org/W1486164486","https://openalex.org/W1506342804","https://openalex.org/W1847986692","https://openalex.org/W1963564197","https://openalex.org/W1980282429","https://openalex.org/W2033559265","https://openalex.org/W2035080386","https://openalex.org/W2059825112","https://openalex.org/W2065607954","https://openalex.org/W2089437293","https://openalex.org/W2094224753","https://openalex.org/W2135959058","https://openalex.org/W2148147555","https://openalex.org/W3106161546"],"related_works":["https://openalex.org/W2026020054","https://openalex.org/W4288333409","https://openalex.org/W2950170321","https://openalex.org/W2355201024","https://openalex.org/W2381807583","https://openalex.org/W2390599191","https://openalex.org/W4238100916","https://openalex.org/W2373948857","https://openalex.org/W2376122632","https://openalex.org/W2361362843"],"abstract_inverted_index":{"Sparse":[0],"matrix-matrix":[1,34],"products":[2,14,35,75],"appear":[3],"in":[4,54,77],"multigrid":[5,63],"solvers":[6],"among":[7],"other":[8],"applications.":[9,79],"Some":[10],"implementations":[11],"of":[12,19,44,51],"these":[13],"require":[15],"the":[16,42,49],"inner":[17],"product":[18],"two":[20],"sparse":[21,33],"vectors.":[22],"In":[23],"this":[24,52],"paper,":[25],"we":[26],"propose":[27],"a":[28],"new":[29],"algorithm":[30],"for":[31,60],"computing":[32],"by":[36],"exploiting":[37],"their":[38],"nonzero":[39],"structure":[40],"through":[41],"process":[43],"graph":[45],"coloring.":[46],"We":[47],"prove":[48],"validity":[50],"technique":[53],"general":[55],"and":[56],"demonstrate":[57],"its":[58],"viability":[59],"examples":[61],"including":[62],"methods":[64],"used":[65],"to":[66],"solve":[67],"boundary":[68],"value":[69],"problems":[70],"as":[71,73],"well":[72],"matrix":[74],"appearing":[76],"unstructured":[78]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
