ACM Transactions on Mathematical Software (TOMS)
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
An updated set of basic linear algebra subprograms (BLAS)
ACM Transactions on Mathematical Software (TOMS)
On the Role of Orthogonality in the GMRES Method
SOFSEM '96 Proceedings of the 23rd Seminar on Current Trends in Theory and Practice of Informatics: Theory and Practice of Informatics
Brook for GPUs: stream computing on graphics hardware
ACM SIGGRAPH 2004 Papers
Rounding error analysis of the classical Gram-Schmidt orthogonalization process
Numerische Mathematik
Implementing sparse matrix-vector multiplication on throughput-oriented processors
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
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We study the numerical behavior of heterogeneous systems such as CPU with GPU or IBM Cell processors for some orthogonalization processes. We focus on the influence of the different floating arithmetic handling of these accelerators with Gram-Schmidt orthogonalization using single and double precision. We observe for dense matrices a loss of at worst 1 digit for CUDA-enabled GPUs as well as a speed-up of 20×, and 2 digits for the Cell processor for a 7× speed-up. For sparse matrices, the result between CPU and GPU is very close and the speed-up is 10×. We conclude that the Cell processor is a good accelerator for double precision because of its full IEEE compliance, and not sufficient for single precision applications. The GPU speed-up is better than Cell and the decent IEEE support delivers results close to the CPU ones for both precisions.