{"id":"https://openalex.org/W3204062674","doi":"https://doi.org/10.1145/3472456.3472484","title":"Tridiagonal GPU Solver with Scaled Partial Pivoting at Maximum Bandwidth","display_name":"Tridiagonal GPU Solver with Scaled Partial Pivoting at Maximum Bandwidth","publication_year":2021,"publication_date":"2021-08-09","ids":{"openalex":"https://openalex.org/W3204062674","doi":"https://doi.org/10.1145/3472456.3472484","mag":"3204062674"},"language":"en","primary_location":{"id":"doi:10.1145/3472456.3472484","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3472456.3472484","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3472456.3472484","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"50th International Conference on Parallel Processing","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3472456.3472484","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007464024","display_name":"Christoph Klein","orcid":"https://orcid.org/0000-0003-2019-6074"},"institutions":[{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Christoph Klein","raw_affiliation_strings":["University of Heidelberg, ZITI, Germany"],"affiliations":[{"raw_affiliation_string":"University of Heidelberg, ZITI, Germany","institution_ids":["https://openalex.org/I223822909"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047006398","display_name":"Robert Strzodka","orcid":"https://orcid.org/0000-0003-0468-0472"},"institutions":[{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Robert Strzodka","raw_affiliation_strings":["University of Heidelberg, ZITI, Germany"],"affiliations":[{"raw_affiliation_string":"University of Heidelberg, ZITI, Germany","institution_ids":["https://openalex.org/I223822909"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5007464024"],"corresponding_institution_ids":["https://openalex.org/I223822909"],"apc_list":null,"apc_paid":null,"fwci":0.4439,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.68025146,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":1.0,"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":1.0,"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":0.9976999759674072,"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"}},{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9901999831199646,"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/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.9347182512283325},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.826213002204895},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6771554946899414},{"id":"https://openalex.org/keywords/tridiagonal-matrix-algorithm","display_name":"Tridiagonal matrix algorithm","score":0.663023829460144},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.6510875225067139},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.47725769877433777},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.4702664315700531},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.45774146914482117},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4569869041442871},{"id":"https://openalex.org/keywords/simd","display_name":"SIMD","score":0.44511425495147705},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3998938202857971},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3895038962364197},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27310216426849365},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.18281441926956177},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.12020713090896606},{"id":"https://openalex.org/keywords/computational-chemistry","display_name":"Computational chemistry","score":0.06528547406196594}],"concepts":[{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.9347182512283325},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.826213002204895},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6771554946899414},{"id":"https://openalex.org/C176603272","wikidata":"https://www.wikidata.org/wiki/Q1819156","display_name":"Tridiagonal matrix algorithm","level":4,"score":0.663023829460144},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.6510875225067139},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.47725769877433777},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.4702664315700531},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.45774146914482117},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4569869041442871},{"id":"https://openalex.org/C150552126","wikidata":"https://www.wikidata.org/wiki/Q339387","display_name":"SIMD","level":2,"score":0.44511425495147705},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3998938202857971},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3895038962364197},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27310216426849365},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.18281441926956177},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.12020713090896606},{"id":"https://openalex.org/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","level":1,"score":0.06528547406196594},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3472456.3472484","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3472456.3472484","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3472456.3472484","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"50th International Conference on Parallel Processing","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/3472456.3472484","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3472456.3472484","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3472456.3472484","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"50th International Conference on Parallel Processing","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3204062674.pdf","grobid_xml":"https://content.openalex.org/works/W3204062674.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1629601946","https://openalex.org/W1974312429","https://openalex.org/W1990523337","https://openalex.org/W2018580582","https://openalex.org/W2035080386","https://openalex.org/W2036506377","https://openalex.org/W2043990347","https://openalex.org/W2047610878","https://openalex.org/W2074554610","https://openalex.org/W2098588961","https://openalex.org/W2100952904","https://openalex.org/W2102512593","https://openalex.org/W2113264898","https://openalex.org/W2141524575","https://openalex.org/W2161456019","https://openalex.org/W2167174057","https://openalex.org/W2278832816","https://openalex.org/W2342186056","https://openalex.org/W2461005004","https://openalex.org/W2731702594","https://openalex.org/W2738229363","https://openalex.org/W2767066575","https://openalex.org/W2806238950","https://openalex.org/W2897406841","https://openalex.org/W2899467728","https://openalex.org/W2966915191","https://openalex.org/W3013265033","https://openalex.org/W3015517561","https://openalex.org/W4205624883","https://openalex.org/W4235310157"],"related_works":["https://openalex.org/W2157863322","https://openalex.org/W2360550119","https://openalex.org/W2001381587","https://openalex.org/W2057923237","https://openalex.org/W4212973497","https://openalex.org/W1980786482","https://openalex.org/W1606194289","https://openalex.org/W4289860553","https://openalex.org/W3477132","https://openalex.org/W1792937979"],"abstract_inverted_index":{"Partial":[0],"pivoting":[1,40],"is":[2,64,85,122],"the":[3,52,62,68,78,81,89,110],"method":[4],"of":[5,29,61,80,103,116,131],"choice":[6],"to":[7,109],"ensure":[8],"stability":[9],"in":[10,46,107],"matrix":[11],"factorizations":[12],"performed":[13],"on":[14,24],"CPUs.":[15],"For":[16,94],"sparse":[17,133],"matrices,":[18],"this":[19],"has":[20],"not":[21],"been":[22],"implemented":[23],"GPUs":[25],"so":[26],"far":[27],"because":[28],"problems":[30,143],"with":[31,99,144],"data-dependent":[32,53],"execution":[33],"flow.":[34],"This":[35],"work":[36],"incorporates":[37],"scaled":[38],"partial":[39],"into":[41],"a":[42,48,126],"tridiagonal":[43,82,113,120],"GPU":[44,83],"solver":[45,84,114,121],"such":[47],"fashion":[49],"that":[50],"despite":[51],"decisions":[54],"no":[55,86],"SIMD":[56],"divergence":[57],"occurs.":[58],"The":[59,118],"cost":[60,79],"computation":[63],"completely":[65],"hidden":[66],"behind":[67],"data":[69,92],"movement":[70],"which":[71],"itself":[72],"runs":[73],"at":[74],"maximum":[75],"bandwidth.":[76],"Therefore,":[77],"more":[87],"than":[88],"minimally":[90],"required":[91],"movement.":[93],"large":[95,132],"single":[96],"precision":[97],"systems":[98],"2^25":[100],"unknowns,":[101],"speedups":[102],"5":[104],"are":[105],"reported":[106],"comparison":[108],"numerically":[111],"stable":[112],"(gtsv2)":[115],"cuSPARSE.":[117],"proposed":[119],"also":[123],"evaluated":[124],"as":[125],"preconditioner":[127],"for":[128,142],"Krylov":[129],"solvers":[130],"linear":[134],"equation":[135],"systems.":[136],"As":[137],"expected":[138],"it":[139],"performs":[140],"best":[141],"strong":[145],"anisotropies.":[146]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
