{"id":"https://openalex.org/W4381327231","doi":"https://doi.org/10.1145/3577193.3593731","title":"Using Additive Modifications in LU Factorization Instead of Pivoting","display_name":"Using Additive Modifications in LU Factorization Instead of Pivoting","publication_year":2023,"publication_date":"2023-06-20","ids":{"openalex":"https://openalex.org/W4381327231","doi":"https://doi.org/10.1145/3577193.3593731"},"language":"en","primary_location":{"id":"doi:10.1145/3577193.3593731","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3577193.3593731","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 37th International Conference on Supercomputing","raw_type":"proceedings-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/A5044449337","display_name":"Neil Lindquist","orcid":"https://orcid.org/0000-0001-9404-3121"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Neil Lindquist","raw_affiliation_strings":["Innovative Computing Laboratory, University of Tennessee, Knoxville, TN, United States of America"],"affiliations":[{"raw_affiliation_string":"Innovative Computing Laboratory, University of Tennessee, Knoxville, TN, United States of America","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073990539","display_name":"Piotr \u0141uszczek","orcid":"https://orcid.org/0000-0002-0089-6965"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Piotr Luszczek","raw_affiliation_strings":["Innovative Computing Laboratory, University of Tennessee, Knoxville, TN, United States of America"],"affiliations":[{"raw_affiliation_string":"Innovative Computing Laboratory, University of Tennessee, Knoxville, TN, United States of America","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075517045","display_name":"Jack Dongarra","orcid":"https://orcid.org/0000-0003-3247-1782"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jack Dongarra","raw_affiliation_strings":["Innovative Computing Laboratory, University of Tennessee, Knoxville, TN, USA"],"affiliations":[{"raw_affiliation_string":"Innovative Computing Laboratory, University of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044449337"],"corresponding_institution_ids":["https://openalex.org/I75027704"],"apc_list":null,"apc_paid":null,"fwci":1.0085,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.79036693,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"14","last_page":"24"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9995999932289124,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9926000237464905,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/gaussian-elimination","display_name":"Gaussian elimination","score":0.8726584911346436},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7072499394416809},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.6716436743736267},{"id":"https://openalex.org/keywords/lu-decomposition","display_name":"LU decomposition","score":0.5965846180915833},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5959126353263855},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.5915594100952148},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.5810960531234741},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.49376019835472107},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.49315160512924194},{"id":"https://openalex.org/keywords/synchronization","display_name":"Synchronization (alternating current)","score":0.4885645806789398},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.48720329999923706},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4846413731575012},{"id":"https://openalex.org/keywords/supercomputer","display_name":"Supercomputer","score":0.48309779167175293},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4292789101600647},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.39231637120246887},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.3715142011642456},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.30581575632095337},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21214962005615234},{"id":"https://openalex.org/keywords/computational-chemistry","display_name":"Computational chemistry","score":0.06683215498924255}],"concepts":[{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.8726584911346436},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7072499394416809},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.6716436743736267},{"id":"https://openalex.org/C123213974","wikidata":"https://www.wikidata.org/wiki/Q833089","display_name":"LU decomposition","level":4,"score":0.5965846180915833},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5959126353263855},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.5915594100952148},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.5810960531234741},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.49376019835472107},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.49315160512924194},{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.4885645806789398},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.48720329999923706},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4846413731575012},{"id":"https://openalex.org/C83283714","wikidata":"https://www.wikidata.org/wiki/Q121117","display_name":"Supercomputer","level":2,"score":0.48309779167175293},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4292789101600647},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.39231637120246887},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3715142011642456},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.30581575632095337},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21214962005615234},{"id":"https://openalex.org/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","level":1,"score":0.06683215498924255},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3577193.3593731","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3577193.3593731","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 37th International Conference on Supercomputing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8557420397","display_name":null,"funder_award_id":"2004541","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W105504140","https://openalex.org/W1274374232","https://openalex.org/W1962219632","https://openalex.org/W1976378297","https://openalex.org/W2020804487","https://openalex.org/W2022486515","https://openalex.org/W2043118877","https://openalex.org/W2051170452","https://openalex.org/W2075066642","https://openalex.org/W2104760562","https://openalex.org/W2108187211","https://openalex.org/W2115780241","https://openalex.org/W2139182243","https://openalex.org/W2163688235","https://openalex.org/W2601355684","https://openalex.org/W2617819327","https://openalex.org/W2752879223","https://openalex.org/W2791341782","https://openalex.org/W2817952343","https://openalex.org/W2963930528","https://openalex.org/W2983126917","https://openalex.org/W3081844928","https://openalex.org/W3131932797","https://openalex.org/W3136816837","https://openalex.org/W3200256640","https://openalex.org/W4236339958","https://openalex.org/W4250649172","https://openalex.org/W4288072583","https://openalex.org/W4320061941"],"related_works":["https://openalex.org/W5176254","https://openalex.org/W1966287322","https://openalex.org/W2561626198","https://openalex.org/W4244491923","https://openalex.org/W3108517195","https://openalex.org/W4224251700","https://openalex.org/W4381327231","https://openalex.org/W4210382808","https://openalex.org/W2790716956","https://openalex.org/W2043246824"],"abstract_inverted_index":{"Direct":[0],"solvers":[1],"for":[2,89,114],"dense":[3],"systems":[4],"of":[5,37,94],"linear":[6,64],"equations":[7],"commonly":[8],"use":[9],"partial":[10,87],"pivoting":[11,17,45,88,113],"to":[12,44,80,104],"ensure":[13],"numerical":[14,48,63],"stability.":[15],"However,":[16],"can":[18],"introduce":[19],"significant":[20],"performance":[21,36,78],"overheads,":[22],"such":[23],"as":[24],"synchronization":[25],"and":[26,67],"data":[27],"movement,":[28],"particularly":[29],"on":[30,70,92],"distributed":[31],"systems.":[32],"To":[33],"improve":[34],"the":[35,71,95],"these":[38],"solvers,":[39],"we":[40],"present":[41],"an":[42],"alternative":[43],"in":[46],"which":[47],"stability":[49],"is":[50],"obtained":[51],"through":[52],"additive":[53],"updates.":[54],"We":[55],"implemented":[56],"this":[57],"approach":[58,75],"using":[59],"SLATE,":[60],"a":[61],"GPU-accelerated":[62],"algebra":[65],"library,":[66],"evaluated":[68],"it":[69],"Summit":[72],"supercomputer.":[73],"Our":[74],"provides":[76,100],"better":[77,101],"(up":[79,103],"5-fold":[81],"speedup)":[82],"than":[83,108],"Gaussian":[84,109],"elimination":[85,110],"with":[86,111],"comparable":[90,115],"accuracy":[91,102],"most":[93],"tested":[96],"matrices.":[97],"It":[98],"also":[99],"15":[105],"more":[106],"digits)":[107],"no":[112],"performance.":[116]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}