Solving Linear Equations with Conjugate Gradient Method on OpenCL Platforms

Caner Sayin
Graduate School of Science and Engineering, Kadir Has University
Kadir Has University, 2012



   author={SAY{.I}N, CANER},



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The parallelism in GPUs offers extremely good performance on a lot of high-performance computing applications. Linear algebra is one of the areas which can benefit from GPU potential. Conjugate Gradient (CG) benchmark is a significant computation in computing applications. It uses conjugate gradient method that offers numerical solutions on specific systems of linear equations. The Conjugate Gradient contains a few scalar operations, reduction of sums and a sparse matrix vector multiplication. Sparse matrix-vector multiplication is the part where the most computation time is spent. In this thesis, we present GPU, Conjugate Gradient (CG) Method, Sparse MatrixVector Multiplication (SpMxV) on Compressed Sparse Row (CSR) format, OpenMP and OpenCL. The aim of the thesis is parallelization of SpMxV on CSR format which is the most costly part of CG and gain some performance by running it on GPU. We use OpenCL that allows writing programs which run across heterogeneous platforms such as CPUs, GPUs and other processors. The experiments show that SpMxV on a GPU with OpenCL spends less time according to SpMxV running on a CPU. Furthermore, OpenMp, which is another parallel programming language, is compared to OpenCL. OpenCL is a bit better than OpenMP at some points.
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