On diagonally structured matrix computation

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dc.contributor.authorMahmud, Mohammad Sakib
dc.contributor.authorUniversity of Lethbridge. Faculty of Arts and Science
dc.contributor.supervisorHossain, Shahadat
dc.date.accessioned2019-12-24T16:35:48Z
dc.date.available2019-12-24T16:35:48Z
dc.date.issued2019
dc.degree.levelMastersen_US
dc.description.abstractIn this thesis, we have proposed efficient implementations of linear algebra kernels such as matrix-vector and matrix-matrix multiplications by formulating arithmetic calculations in terms of diagonals and thereby giving an orientation-neutral (column-/row-major layout) computational scheme. Matrix elements are accessed with stride-1 and no indirect referencing is involved. Access to the transposed matrix requires no additional effort. The proposed storage scheme handles dense matrices and matrices with special structures such as banded, symmetric in a uniform manner. Test results from numerical experiments with OpenMP implementation are promising. We also show that, using our diagonal framework, Java native arrays can yield superior computational performance. We present two alternative implementations for matrix-matrix multiplication operation in Java. The results from numerical testing demonstrate the advantage of our proposed methods.en_US
dc.identifier.urihttps://hdl.handle.net/10133/5649
dc.language.isoen_USen_US
dc.proquest.subject0984en_US
dc.proquest.subject0537en_US
dc.proquest.subject0800en_US
dc.proquestyesYesen_US
dc.publisherLethbridge, Alta. : Universtiy of Lethbridge, Department of Mathematics and Computer Scienceen_US
dc.publisher.departmentDepartment of Mathematics and Computer Scienceen_US
dc.publisher.facultyArts and Scienceen_US
dc.relation.ispartofseriesThesis (University of Lethbridge. Faculty of Arts and Science)en_US
dc.subjectdense matricesen_US
dc.subjectdiagonal storageen_US
dc.subjectlinear algebra kernalsen_US
dc.subjectmatrix-matrix multiplicationsen_US
dc.subjectmatrix-vector multiplicationsen_US
dc.subjectorientation-neutral computationen_US
dc.subjectAlgebras, Linear -- Data processingen_US
dc.subjectMatrices -- Data processingen_US
dc.subjectParallel processing (Electronic computers)en_US
dc.subjectMemory management (Computer science)en_US
dc.subjectDissertations, Academicen_US
dc.titleOn diagonally structured matrix computationen_US
dc.typeThesisen_US
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