LU and QR Factorization on GPUs for High-performance

Abstract

GPUs have become very interesting, especially with the General Purpose Graphics Processing Units. With the ability to program the GPUs, their computation capabilities with the processing power and their competitive low cost have enabled the development of numerous kinds of interesting GPGPU application programs resulting in substantial accomplishments in terms of the performance. The LU and QR factorizations represent an underlying process of a large number of scientific application programs with complex and computationally expensive modules. But in here, the solution process has a high impact on the matrix size for the performance because of the costly computations. Proposed methodology for the GPU only LU and QR factorization algorithms were implemented using block matrix factorization where the input matrix is considered as multiple matrices when performing the factorization steps. GPU only factorization algorithms are implemented on a NVIDIA MX130 GPU. For LU factorization, the suggested GPU only algorithm implementation starts to perform well with the square matrix 6144 and upwards. With the suggested GPU only QR factorization implementation, it was possible to execute matrix sizes up-to 1024x1024. The evaluation of the implemented algorithms clearly depicted that the output matrices are accurate when computed and compared with the input matrix. Finally, it is believed that the work accomplished through this research work has facilitated for the betterment of the learning community as well as the parallel computing and computer science research community