Mixed precision CGS algorithm based on GPU

作者：Li Ximing; Ouyang Dantong; Bai Hongtao^*

来源：Chinese Journal of Scientific Instrument, 2012, 33(1): 97-104.

• Conjugate gradient
• Double precision
• Floating points
• Gauss-Seidel iteration method
• Graphics Processing Unit
• Inner iteration
• Jacobi iteration
• Mixed precision
• Numerical algorithms
• Outer iteration
• Speedup ratio
• Whole process

GPU-based numerical algorithms have the shortcoming of low performance for double precision. We suggest a mixed precision conjugate gradient squared algorithm suitable for the GPU of Fermi-CUDA to solve sparse linear equations. The scheme uses a combination of single-precision inner iteration and double-precision outer iteration to take the advantages of efficient single-precision operation and accurate double-precision operation under the GPU structure. The calculation of the algorithm is implemented entirely on the GPU, which reduces the data transfer between CPU and GPU. Conjugate gradient squared algorithm, Jacobi iteration method and Gauss-Seidel iteration method based on GPU are implemented; and as inner iteration operators, their influence on the convergence of the whole process is analyzed. Experiments indicate that the mixed precision scheme maintains the native double-precision accuracy of data processing. At the same time, the floating point accuracy is improved by a factor of 2 compared with that using double-precision alone, and the maximum speedup ratio reaches to more than 70.

• 出版日期2012