{"id":{"repo_id":"utc","oai_identifier":"oai:scholar.utc.edu:theses-1853"},"canonical_url":"https://search.dev.ndltd.org/etd/utc/oai:scholar.utc.edu:theses-1853","repository":{"repo_id":"utc","name":"University of Tennessee - Chattanooga","base_url":"https://scholar.utc.edu/do/oai/"},"display":{"title":"Second-generation polyalgorithms for parallel dense-matrix multiplication","abstract":"The polyalgorithm library, originally designed in 1991-1993 by Robert Falgout, Jin Li, and Anthony Skjellum, includes fourteen dense matrix multiplication algorithms mapped onto two-dimensional process grids using the Message Passing Interface (MPI). This thesis' goal is to achieve optimized performance of parallel, dense linear algebra algorithms by varying the algorithm as a function of problem size, shape, data layout, concurrency, and architecture. We integrate these algorithms with an intra-node BLAS DGEMM kernel designed by Thomas Hines (Tennessee Tech), which improves the BLAS DGEMM performance in fat-by-thin dense matrix multiplication region. We add a rank-k-based SUMMA algorithm, which performs better than rank-1-based SUMMA. We studied performance on two cluster systems and results show the performance and improvements achieved. We compare and contrast our results with COSMA, a recent, highly optimized approach, and verify that COSMA, using optimal 3D grid decompositions, has significant advantages provided its preferred data layouts can be used.","abstract_html":"The polyalgorithm library, originally designed in 1991-1993 by Robert Falgout, Jin Li, and Anthony Skjellum, includes fourteen dense matrix multiplication algorithms mapped onto two-dimensional process grids using the Message Passing Interface (MPI). This thesis' goal is to achieve optimized performance of parallel, dense linear algebra algorithms by varying the algorithm as a function of problem size, shape, data layout, concurrency, and architecture. We integrate these algorithms with an intra-node BLAS DGEMM kernel designed by Thomas Hines (Tennessee Tech), which improves the BLAS DGEMM performance in fat-by-thin dense matrix multiplication region. We add a rank-k-based SUMMA algorithm, which performs better than rank-1-based SUMMA. We studied performance on two cluster systems and results show the performance and improvements achieved. We compare and contrast our results with COSMA, a recent, highly optimized approach, and verify that COSMA, using optimal 3D grid decompositions, has significant advantages provided its preferred data layouts can be used.","abstract_has_math":false,"creators":["Nansamba, Grace"],"institution":"University of Tennessee at Chattanooga","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Skjellum, Anthony","Kandah, Farah; Ward, Michael","College of Engineering and Computer Science"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T05:46:59Z","subjects":["Mathematical optimization","Multiplication, Complex"],"languages":["English","eng"],"rights":[],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://scholar.utc.edu/theses/680","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Skjellum, Anthony","Kandah, Farah; Ward, Michael","College of Engineering and Computer Science"]},{"key":"dc:creator","label":"Author","values":["Nansamba, Grace"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-12-01T08:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"]},{"key":"dc:relation","label":"Dc Relation","values":["Masters Theses and Doctoral Dissertations"]},{"key":"dc:type","label":"Dc Type","values":["Masters theses","Text"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematical optimization","Multiplication, Complex"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholar.utc.edu/theses/680"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Dept. of Computer Science and Engineering","M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science."]},{"key":"dc:description.abstract","label":"Abstract","values":["The polyalgorithm library, originally designed in 1991-1993 by Robert Falgout, Jin Li, and Anthony Skjellum, includes fourteen dense matrix multiplication algorithms mapped onto two-dimensional process grids using the Message Passing Interface (MPI). This thesis' goal is to achieve optimized performance of parallel, dense linear algebra algorithms by varying the algorithm as a function of problem size, shape, data layout, concurrency, and architecture. We integrate these algorithms with an intra-node BLAS DGEMM kernel designed by Thomas Hines (Tennessee Tech), which improves the BLAS DGEMM performance in fat-by-thin dense matrix multiplication region. We add a rank-k-based SUMMA algorithm, which performs better than rank-1-based SUMMA. We studied performance on two cluster systems and results show the performance and improvements achieved. We compare and contrast our results with COSMA, a recent, highly optimized approach, and verify that COSMA, using optimal 3D grid decompositions, has significant advantages provided its preferred data layouts can be used."]},{"key":"dc:title","label":"Title","values":["Second-generation polyalgorithms for parallel dense-matrix multiplication"]}]}],"canonical_facts":{"dc:contributor":["Skjellum, Anthony","Kandah, Farah; Ward, Michael","College of Engineering and Computer Science"],"dc:creator":["Nansamba, Grace"],"dc:date":["2020-12-01T08:00:00Z"],"dc:description":["Dept. of Computer Science and Engineering","M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science."],"dc:description.abstract":["The polyalgorithm library, originally designed in 1991-1993 by Robert Falgout, Jin Li, and Anthony Skjellum, includes fourteen dense matrix multiplication algorithms mapped onto two-dimensional process grids using the Message Passing Interface (MPI). This thesis' goal is to achieve optimized performance of parallel, dense linear algebra algorithms by varying the algorithm as a function of problem size, shape, data layout, concurrency, and architecture. We integrate these algorithms with an intra-node BLAS DGEMM kernel designed by Thomas Hines (Tennessee Tech), which improves the BLAS DGEMM performance in fat-by-thin dense matrix multiplication region. We add a rank-k-based SUMMA algorithm, which performs better than rank-1-based SUMMA. We studied performance on two cluster systems and results show the performance and improvements achieved. We compare and contrast our results with COSMA, a recent, highly optimized approach, and verify that COSMA, using optimal 3D grid decompositions, has significant advantages provided its preferred data layouts can be used."],"dc:identifier":["https://scholar.utc.edu/theses/680"],"dc:language":["English","eng"],"dc:publisher":["University of Tennessee at Chattanooga","Chattanooga (Tenn.)"],"dc:relation":["Masters Theses and Doctoral Dissertations"],"dc:rights":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Mathematical optimization","Multiplication, Complex"],"dc:title":["Second-generation polyalgorithms for parallel dense-matrix multiplication"],"dc:type":["Masters theses","Text"]},"updated_at":"2026-07-24T05:46:59Z"}