2026-09-20T04:12:46.000465200Zhttps://opus.uleth.ca/server/oai/requestoai:opus.uleth.ca:10133/56492019-12-25T07:07:25Zcom_10133_3346com_10133_1com_10133_296col_10133_3347col_10133_298
ULethbridge OPUS Repository
supervisor
Hossain, Shahadat
author
Mahmud, Mohammad Sakib
author
University of Lethbridge. Faculty of Arts and Science
2019-12-24T16:35:48Z
2019-12-24T16:35:48Z
2019
https://hdl.handle.net/10133/5649
In 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
dense matrices
diagonal storage
linear algebra kernals
matrix-matrix multiplications
matrix-vector multiplications
orientation-neutral computation
Algebras, Linear -- Data processing
Matrices -- Data processing
Parallel processing (Electronic computers)
Memory management (Computer science)
Dissertations, Academic
On diagonally structured matrix computation
Thesis
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URL
http://localhost:4000/bitstreams/6c92116b-42ff-4e20-b0bd-d9e8e26a9a4a/download
File
MD5
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application/pdf
Mahmud_MohammadSakib_MSC_2019.pdf
URL
http://localhost:4000/bitstreams/10f36410-7d8d-42ca-af70-c83c82c14bf1/download
File
MD5
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text/plain
Mahmud_MohammadSakib_MSC_2019.pdf.txt