# Performance of Linear Algebra Factorization in Multi-Accelerator Architectures

## DOI:

https://doi.org/10.51408/1963-0115## Keywords:

MAGMA, multiple GPU, Linear Algebra, Factorizations## Abstract

Hardware and software are required to effectively solve problems in many domains. The idea of creating a hybrid architecture based on graphics processors arose to meet the increasing demands of modern scientific problems. Most of these problems are reduced to solving linear algebra problems. A set of efficient linear solutions has been successfully used to solve important scientific problems for many years. Factorizations play a crucial role in solving linear algebra problems.

This work presents implementations of LU, QR and Cholesky factorizations on two graphics processors using the MAGMA 2.6.0 library. Their performances are given for matrices with real and complex numbers in single and double precision.

## References

NVIDIA, “NVIDIA CUDA Parallel Computing Platform”. http://www.nvidia.com/object/cuda_home_new.html, NVIDIA, 2013.

International Business Machines Corporation. System/360 Scientific Subroutine Package (360A-CM-03X) Version II, Programmer’s Manual. IBM Technical Publications Department, White Plains, NY, 1967.

B. S. Garbow. EISPACK-a package of matrix eigensystem routines. Computer Physics Communications, 7(4):179–184, 1974.

C. L. Lawson, R. J. Hanson, D. R. Kincaid, and F. T. Krogh. Basic Linear Algebra Subprograms for Fortran Usage. ACM Trans. Math. Softw., 5(3):308–323, September 1979.

R. J. Hanson, F. T. Krogh, and C. L. Lawson. A proposal for standard linear algebra subprograms. ACM Signum Newsletter, 1973.

J. Dongarra, C. B. Moler, J. R. Bunch, and G. W. Stewart. LINPACK Users’ Guide, volume 8. SIAM, 1979.

J. Dongarra, J. Du Croz, S. Hammarling, and R. J. Hanson. Algorithm 656: an extended set of basic linear algebra subprograms: model implementation and test programs. ACM Transactions on Mathematical Software (TOMS), 14(1):18–32, 1988.

Dongarra, J. Du Croz, S. Hammarling, and R. J. Hanson. An Extended Set of FORTRAN Basic Linear Algebra Subprograms. ACM Trans. Math. Softw., 14(1):1–17, March 1988.

E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen. LAPACK Users’ Guide. Society for Industrial and Applied Mathematics, Philadelphia, PA, third edition, 1999.

CUDA Nvidia. Cublas library. NVIDIA Corporation, Santa Clara, California, 15, 2008.

J. R. Humphrey, D. K. Price, K. E. Spagnoli, A. L. Paolini, and E. J. Kelmelis. CULA: hybrid GPU accelerated linear algebra routines. In SPIE Defense, Security, and Sensing, pages 770502–770502. International Society for Optics and Photonics, 2010.

“MAGMA Matrix Algebra on GPU and Multicore Architectures”, http://icl.cs.utk.edu/magma/, 2014.

H. V. Astsatryan, E. E. Gichunts, “Performances of Methods for Solving a Linear System of Equations in the Architecture of GPU Accelerator”, Transactions of IIAP NAS RA, Mathematical Problems of Computer Science, vol. 45, pp. 44—52, 2016.

B. N. Parlett, The Symmetric Eigenvalue Problem. Englewood Cliffs, NJ: Prentice-Hall, 1980.

G. H.Golub, C. F. V.Loan, Matrix Computations, 3rd ed. Baltimore: The Johns Hopkins University Press, 1996.

## Downloads

## Published

## How to Cite

*Mathematical Problems of Computer Science*,

*61*, 62–69. https://doi.org/10.51408/1963-0115

## Issue

## Section

## License

Copyright (c) 2024 Edita E. Gichunts

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.