{"id":"https://openalex.org/W7220737887","doi":"https://doi.org/10.48550/arxiv.2610.06414","title":"A Mixed-Precision Model for Matrix-Splitting Methods","display_name":"A Mixed-Precision Model for Matrix-Splitting Methods","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220737887","doi":"https://doi.org/10.48550/arxiv.2610.06414"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.06414","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06414","pdf_url":"https://arxiv.org/pdf/2610.06414","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.06414","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044449337","display_name":"Neil Lindquist","orcid":"https://orcid.org/0000-0001-9404-3121","observed_orcids":["https://orcid.org/0000-0001-9404-3121"]},"institutions":[{"id":"https://openalex.org/I4210127875","display_name":"Nvidia (United States)","ror":"https://ror.org/03jdj4y14","country_code":"US","type":"company","lineage":["https://openalex.org/I4210127875"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lindquist, Neil","raw_affiliation_strings":["NVIDIA , CA , USA 95051"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NVIDIA , CA , USA 95051","institution_ids":["https://openalex.org/I4210127875"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055298466","display_name":"David Appelhans","orcid":"https://orcid.org/0000-0003-1433-9198","observed_orcids":["https://orcid.org/0000-0003-1433-9198"]},"institutions":[{"id":"https://openalex.org/I4210127875","display_name":"Nvidia (United States)","ror":"https://ror.org/03jdj4y14","country_code":"US","type":"company","lineage":["https://openalex.org/I4210127875"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Appelhans, David","raw_affiliation_strings":["NVIDIA , CA , USA 95051"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NVIDIA , CA , USA 95051","institution_ids":["https://openalex.org/I4210127875"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157665037","display_name":"Chales W. Jackson","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1319063186","display_name":"Langley Research Center","ror":"https://ror.org/0399mhs52","country_code":"US","type":"facility","lineage":["https://openalex.org/I1319063186","https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jackson, Chales W.","raw_affiliation_strings":["NASA Langley Research Center , VA USA , 23681"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NASA Langley Research Center , VA USA , 23681","institution_ids":["https://openalex.org/I1319063186"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068624171","display_name":"Joseph M. Derlaga","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1319063186","display_name":"Langley Research Center","ror":"https://ror.org/0399mhs52","country_code":"US","type":"facility","lineage":["https://openalex.org/I1319063186","https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Derlaga, Joseph M.","raw_affiliation_strings":["NASA Langley Research Center , VA USA , 23681"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NASA Langley Research Center , VA USA , 23681","institution_ids":["https://openalex.org/I1319063186"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9634000062942505,"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":0.9634000062942505,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.02160000056028366,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.013700000010430813,"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/mixed-precision","display_name":"mixed precision","score":0.902999997138977},{"id":"https://openalex.org/keywords/stationary-iterative-methods","display_name":"stationary iterative methods","score":0.8960000276565552},{"id":"https://openalex.org/keywords/memory-bound-performance","display_name":"memory-bound performance","score":0.6959999799728394},{"id":"https://openalex.org/keywords/data-movement-reduction","display_name":"data movement reduction","score":0.8740000128746033},{"id":"https://openalex.org/keywords/iterative-refinement","display_name":"iterative refinement","score":0.7889999747276306},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.8320000171661377},{"id":"https://openalex.org/keywords/block-gauss-seidel","display_name":"block Gauss-Seidel","score":0.9959999918937683},{"id":"https://openalex.org/keywords/overflow","display_name":"overflow","score":0.656000018119812},{"id":"https://openalex.org/keywords/compressible-fluid-dynamics","display_name":"compressible fluid dynamics","score":0.8330000042915344},{"id":"https://openalex.org/keywords/arithmetic-intensity","display_name":"arithmetic intensity","score":0.6029999852180481}],"concepts":[{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.8992000222206116},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.6482999920845032},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6273000240325928},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.6008999943733215},{"id":"https://openalex.org/C67923128","wikidata":"https://www.wikidata.org/wiki/Q1481893","display_name":"Jacobi method","level":2,"score":0.5611000061035156},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49129998683929443},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4909999966621399},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.48590001463890076},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4352000057697296},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3562999963760376},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.31209999322891235},{"id":"https://openalex.org/C143587482","wikidata":"https://www.wikidata.org/wiki/Q1543216","display_name":"Iterative and incremental development","level":2,"score":0.30880001187324524},{"id":"https://openalex.org/C2779982483","wikidata":"https://www.wikidata.org/wiki/Q6094420","display_name":"Iterative refinement","level":2,"score":0.2939000129699707},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.28519999980926514},{"id":"https://openalex.org/C202799725","wikidata":"https://www.wikidata.org/wiki/Q272035","display_name":"Accuracy and precision","level":2,"score":0.27469998598098755}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.06414","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06414","pdf_url":"https://arxiv.org/pdf/2610.06414","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.06414","doi":"https://doi.org/10.48550/arxiv.2610.06414","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.06414","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.06414","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06414","pdf_url":"https://arxiv.org/pdf/2610.06414","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306101","display_name":"National Aeronautics and Space Administration","ror":"https://ror.org/027ka1x80"},{"id":"https://openalex.org/F4320332378","display_name":"Langley Research Center","ror":"https://ror.org/0399mhs52"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220737887.pdf","grobid_xml":"https://content.openalex.org/works/W7220737887.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7096551381","https://openalex.org/W3176827258","https://openalex.org/W4212968661","https://openalex.org/W2323200980","https://openalex.org/W3213194041","https://openalex.org/W2773909359","https://openalex.org/W1555680562","https://openalex.org/W4404404789","https://openalex.org/W2555266989","https://openalex.org/W4315695022"],"abstract_inverted_index":{"The":[0],"performance":[1],"of":[2,24,59,98],"stationary":[3],"iterative":[4,29,67],"methods":[5],"is":[6],"memory-bound,":[7],"due":[8],"to":[9,20,72,76,89,137],"the":[10,22,53,57,60,74,115,118,138],"low":[11],"arithmetic":[12],"intensity.":[13],"So,":[14],"we":[15,64,83,113],"propose":[16],"a":[17,44,124,134],"mixed-precision":[18],"technique":[19,39],"reduce":[21],"amount":[23],"data":[25],"movement":[26],"in":[27,117],"matrix-splitting":[28],"methods.":[30],"We":[31],"demonstrate":[32,65],"both":[33],"theoretically":[34],"and":[35,56,86,102,105,109,132],"experimentally":[36],"that":[37,66],"this":[38,81],"will":[40],"generally":[41],"converge":[42],"at":[43],"similar":[45],"rate":[46],"as":[47],"an":[48,91],"exact-precision":[49],"iteration,":[50],"depending":[51],"on":[52],"precision":[54,88,97,116],"used":[55,71,121],"conditioning":[58],"$M$":[61],"matrix.":[62],"Furthermore,":[63,112],"refinement":[68],"can":[69],"be":[70],"refine":[73],"solution":[75],"full":[77],"double-precision":[78],"accuracy.":[79],"Using":[80],"approach,":[82],"mixed":[84],"half":[85],"double":[87,96],"achieve":[90],"average":[92],"speedup":[93,136],"over":[94],"uniform":[95],"$1.60\\times$":[99],"for":[100,107,127],"scalar":[101,108],"block":[103,110],"Jacobi":[104],"$1.25\\times$":[106],"Gauss-Seidel.":[111],"reduced":[114],"SSOR":[119],"iteration":[120],"by":[122],"OVERFLOW,":[123],"NASA":[125],"code":[126],"compressible":[128],"fluid":[129],"dynamics":[130],"simulations,":[131],"achieved":[133],"$1.14\\times$":[135],"overall":[139],"application.":[140]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-07T00:00:00"}