{"id":"https://openalex.org/W2912699192","doi":"https://doi.org/10.1145/3232850","title":"Hierarchical Matrix Operations on GPUs","display_name":"Hierarchical Matrix Operations on GPUs","publication_year":2019,"publication_date":"2019-02-24","ids":{"openalex":"https://openalex.org/W2912699192","doi":"https://doi.org/10.1145/3232850","mag":"2912699192"},"language":"en","primary_location":{"id":"doi:10.1145/3232850","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3232850","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"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 Mathematical Software","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/A5088105630","display_name":"Wajih Boukaram","orcid":"https://orcid.org/0000-0002-2958-9344"},"institutions":[{"id":"https://openalex.org/I4210099236","display_name":"Kootenay Association for Science & Technology","ror":"https://ror.org/011pv9p44","country_code":"CA","type":"nonprofit","lineage":["https://openalex.org/I4210099236"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Wajih Boukaram","raw_affiliation_strings":["Extreme Computing Research Center, KAUST"],"raw_orcid":"https://orcid.org/0000-0002-2958-9344","affiliations":[{"raw_affiliation_string":"Extreme Computing Research Center, KAUST","institution_ids":["https://openalex.org/I4210099236"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066773923","display_name":"George Turkiyyah","orcid":"https://orcid.org/0000-0002-1692-5812"},"institutions":[{"id":"https://openalex.org/I98635879","display_name":"American University of Beirut","ror":"https://ror.org/04pznsd21","country_code":"LB","type":"education","lineage":["https://openalex.org/I98635879"]}],"countries":["LB"],"is_corresponding":false,"raw_author_name":"George Turkiyyah","raw_affiliation_strings":["American University of Beirut, Lebanon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"American University of Beirut, Lebanon","institution_ids":["https://openalex.org/I98635879"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021283893","display_name":"David E. Keyes","orcid":"https://orcid.org/0000-0002-4052-7224"},"institutions":[{"id":"https://openalex.org/I4210099236","display_name":"Kootenay Association for Science & Technology","ror":"https://ror.org/011pv9p44","country_code":"CA","type":"nonprofit","lineage":["https://openalex.org/I4210099236"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"David Keyes","raw_affiliation_strings":["Extreme Computing Research Center, KAUST"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Extreme Computing Research Center, KAUST","institution_ids":["https://openalex.org/I4210099236"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.07,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.94269037,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"45","issue":"1","first_page":"1","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9987999796867371,"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":0.9987999796867371,"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":0.9984999895095825,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6640645265579224},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.5837021470069885},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.5508086681365967},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.5352905988693237},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4729345142841339},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.46422216296195984},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4524303078651428},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4407033920288086},{"id":"https://openalex.org/keywords/algebraic-operation","display_name":"Algebraic operation","score":0.4340173006057739},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40005677938461304},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.26893484592437744},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.2547835409641266}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6640645265579224},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.5837021470069885},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.5508086681365967},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.5352905988693237},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4729345142841339},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.46422216296195984},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4524303078651428},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4407033920288086},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.4340173006057739},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40005677938461304},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26893484592437744},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.2547835409641266},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3232850","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3232850","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"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 Mathematical Software","raw_type":"journal-article"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/652969","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/652969","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8444106020","display_name":null,"funder_award_id":"NPRP-5-995-2-415","funder_id":"https://openalex.org/F4320332753","funder_display_name":"Qatar National Research Fund"}],"funders":[{"id":"https://openalex.org/F4320309480","display_name":"Nvidia","ror":"https://ror.org/03jdj4y14"},{"id":"https://openalex.org/F4320332753","display_name":"Qatar National Research Fund","ror":"https://ror.org/01svaqq28"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W36826159","https://openalex.org/W1480958225","https://openalex.org/W1569304948","https://openalex.org/W1584657480","https://openalex.org/W1602760118","https://openalex.org/W1839773802","https://openalex.org/W1976016599","https://openalex.org/W1985263109","https://openalex.org/W1991324025","https://openalex.org/W1992615353","https://openalex.org/W2008515709","https://openalex.org/W2010717035","https://openalex.org/W2016075148","https://openalex.org/W2018419001","https://openalex.org/W2037870010","https://openalex.org/W2040740620","https://openalex.org/W2042112576","https://openalex.org/W2088536107","https://openalex.org/W2089958289","https://openalex.org/W2122137889","https://openalex.org/W2128853364","https://openalex.org/W2188296733","https://openalex.org/W2232944345","https://openalex.org/W2298381282","https://openalex.org/W2528745529","https://openalex.org/W2559809597","https://openalex.org/W2561373036","https://openalex.org/W2570841452","https://openalex.org/W2583849828","https://openalex.org/W2736056409","https://openalex.org/W2949076165","https://openalex.org/W2963754333","https://openalex.org/W2964186186","https://openalex.org/W3031997026"],"related_works":["https://openalex.org/W3147497457","https://openalex.org/W3121314575","https://openalex.org/W4206336957","https://openalex.org/W4225552076","https://openalex.org/W1973961853","https://openalex.org/W3004823601","https://openalex.org/W4285303061","https://openalex.org/W4379518721","https://openalex.org/W2138414916","https://openalex.org/W1561856806"],"abstract_inverted_index":{"Hierarchical":[0],"matrices":[1,9,70,242],"are":[2,119],"space-":[3],"and":[4,34,60,91,104,113,175,230,245,265],"time-efficient":[5],"representations":[6,29,90],"of":[7,15,21,41,46,56,68,123],"dense":[8,47],"that":[10,30,96,170,190,210],"exploit":[11],"the":[12,42,64,81,88,111,121,129,165,172,176,183,202,217,252,261,272,276],"low-rank":[13,25],"structure":[14],"matrix":[16,57],"blocks":[17],"at":[18,120],"different":[19],"levels":[20],"granularity.":[22],"The":[23,73,155],"hierarchically":[24],"block":[26,83,89,144],"partitioning":[27],"produces":[28],"can":[31],"be":[32,197,214],"stored":[33],"operated":[35],"on":[36,71,185,240,275],"in":[37,78,93,135,157,188,207,268],"near-linear":[38],"complexity":[39,45,109],"instead":[40],"usual":[43],"polynomial":[44],"matrices.":[48],"In":[49],"this":[50],"article,":[51],"we":[52],"present":[53],"high-performance":[54],"implementations":[55],"vector":[58],"multiplication":[59],"compression":[61,114,273],"operations":[62,118,125,195,221],"for":[63,87,110,126,145,260,271],"H":[65,74],"2":[66,75],"variant":[67,76],"hierarchical":[69,82,85,127,173],"GPUs.":[72],"exploits,":[77],"addition":[79],"to":[80,178,181,196,213],"partitioning,":[84],"bases":[86],"results":[92,239],"a":[94,132,141,208,232],"scheme":[95],"requires":[97,200],"only":[98,222],"O":[99,105],"(":[100,106],"n":[101,107],")":[102,108],"storage":[103],"mat-vec":[112,130],"kernels.":[115],"These":[116],"two":[117],"core":[122],"algebraic":[124,147],"matrices,":[128],"being":[131],"ubiquitous":[133],"operation":[134,264,274],"numerical":[136,238],"algorithms":[137,161],"while":[138],"compression/recompression":[139],"represents":[140],"key":[142,177],"building":[143],"other":[146],"operations,":[148],"which":[149],"require":[150],"periodic":[151],"recompression":[152],"during":[153],"execution.":[154],"difficulties":[156],"developing":[158],"efficient":[159],"GPU":[160],"come":[162],"primarily":[163],"from":[164,243,248],"irregular":[166],"tree":[167],"data":[168,206,228],"structures":[169],"underlie":[171],"representations,":[174],"performance":[179,270],"is":[180],"recast":[182],"computations":[184],"flattened":[186],"trees":[187],"ways":[189],"allow":[191],"batched":[192,218],"linear":[193],"algebra":[194],"performed.":[198],"This":[199],"marshaling":[201],"irregularly":[203],"laid":[204],"out":[205],"way":[209],"allows":[211],"them":[212],"used":[215],"by":[216],"routines.":[219],"Marshaling":[220],"involve":[223],"pointer":[224],"arithmetic":[225],"with":[226],"no":[227],"movement":[229],"as":[231],"result":[233],"have":[234],"minimal":[235],"overhead.":[236],"Our":[237],"covariance":[241],"2D":[244],"3D":[246],"problems":[247],"spatial":[249],"statistics":[250],"show":[251],"high":[253],"efficiency":[254],"our":[255],"routines":[256],"achieve":[257],"over":[258,266],"550GB/s":[259],"bandwidth-limited":[262],"matrix-vector":[263],"850GFLOPS/s":[267],"sustained":[269],"P100":[277],"Pascal":[278],"GPU.":[279]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}