Abstract
Matrix-matrix multiplication is an important linear algebra operation with a myriad of applications in scientific and engineering computing. Due to the relevance and inner parallelism of this operation, there exist many high performance implementations for a variety of hardware platforms. Exploit the structure of the matrices involved in the operation in general provides relevant time and memory savings. This is the case, e.g., when one of the matrices is a symmetric band matrix. This work presents two efficient specialized implementations of the operation when a symmetric band matrix is involved and the target architecture contains a graphics processor (GPU). In particular, both implementations exploit the structure of the matrices to leverage the vast parallelism of the underlying hardware. The experimental results show remarkable reductions in the computation time over the tuned implementations of the same operation provided by MKL and CUBLAS.
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References
Anderson, E., Bai, Z., Demmel, J., Dongarra, J.E., DuCroz, J., Greenbaum, A., Hammarling, S., McKenney, A.E., Ostrouchov, S., Sorensen, D.: LAPACK Users’ Guide. SIAM, Philadelphia (1992)
Benner, P., Dufrechou, E., Ezzatti, P., Igounet, P., Quintana-Ortí, E.S., Remón, A.: Accelerating band linear algebra operations on gPUs with application in model reduction. In: Murgante, B., Misra, S., Rocha, A.M.A.C., Torre, C., Rocha, J.G., Falcão, M.I., Taniar, D., Apduhan, B.O., Gervasi, O. (eds.) ICCSA 2014, Part VI. LNCS, vol. 8584, pp. 386–400. Springer, Heidelberg (2014)
Cuthill, E., McKee, J.: Reducing the bandwidth of sparse symmetric matrices. In: Proceedings of the 1969 24th National Conference, ACM 1969, pp. 157–172. ACM, New York (1969)
Du Croz, J., Mayes, P., Radicati, G.: Factorization of band matrices using level 3 BLAS. LAPACK Working Note 21, Technical Report CS-90-109, University of Tennessee (July 1990)
Dufrechou, E., Ezzatti, P., Quintana-Ortí, E.S., Remón, A.: Accelerating the LYAPACK library using GPUs. J. Supercomput. 65(3), 1114–1124 (2013)
Golub, G., Loan, C.V.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)
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Dufrechou, E., Ezzatti, P., Quintana-Ortí, E.S., Remón, A. (2014). Efficient Symmetric Band Matrix-Matrix Multiplication on GPUs. In: Hernández, G., et al. High Performance Computing. CARLA 2014. Communications in Computer and Information Science, vol 485. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45483-1_1
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DOI: https://doi.org/10.1007/978-3-662-45483-1_1
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