Out-of-core solution of linear systems on graphics processors

Abstract

We combine two high-level application programming interfaces to solve large-scale linear systems with the data stored on disk using current graphics processors (GPU). The result is a simple yet powerful tool that enables a fast development of object-oriented codes, implemented as Matlab M-scripts, for linear algebra operations.

The approach enhances the programmability of the solutions in this problem domain while unleashing the high performance of GPU. Experimental results are reported from Octave, linked with the implementation of basic linear algebra subprograms by Nvidia; as an additional novelty, we evaluate the performance of our approach for the Nvidia new double-precision graphics hardware.

Keywords:

• out-of-core computing
• linear algebra
• high-level APIs
• user-friendly problem-solution environments
• graphics processors

Acknowledgements

This research was partially sponsored by NSF Grants CCF-0540926 and CCF-0702714. The researchers at the Universidad Jaime I of Castellón were supported by the CICYT project TIN2008-06570-C04-01 and FEDER, and projects No. P1-1B2007-19 and P1-1B2007-32 of the Fundación Caixa-Castellón/Bancaixa and UJI. We thank the other members of the FLAME team for their support.

Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).

We thank NVIDIA for the generous donation of equipment that was used in the experiments.

Notes

^1. [email protected]

^2. [email protected]

^3. [email protected]

^4. [email protected]

^5. [email protected]

^6. [email protected]

^7. [email protected]

^8. Billion of floating-point operations per second.

Additional information

Notes on contributors

Maribel Castillo

1. 1. [email protected]

Mercedes Marqués

2. 2. [email protected]

Rafael Mayo

3. 3. [email protected]

Enrique S. Quintana-Ortí

4. 4. [email protected]

Gregorio Quintana-Ortí

5. 5. [email protected]

Rafael Rubio

6. 6. [email protected]

Robert van de Geijn

7. 7. [email protected]