Numerical Behavior of Mixed Precision Iterative Refinement Using the BiCGSTAB Method
Yingqi Zhao, Takeshi Fukaya, Takeshi Iwashita · Journal of Information Processing · 2023
Mixed precision numerical methods using low precision computing have attracted much attention under recent computational hardware trends. In this research, we focus on solving large, sparse, and non-symmetric linear systems, and consider developing a numerical method based on a mixed precision variant of the iterative refinement scheme (MP-IR), in which we can exploit low precision computing and provide a computed solution with the same accuracy as that obtained by conventional methods without low precision computing. We employ the BiCGSTAB solver with FP32 as an inner solver of MP-IR and investigate its numerical behavior through numerical experiments. From the analyses on the obtained results including a comparison with MP-IR using GMRES(m), which is also known as MP-GMRES(m) and has been widely studied, the potential of MP-IR using BiCGSTAB has been confirmed. Together with other obtained results, this paper provides insights that are helpful in developing an efficient mixed precision linear solver for practical applications.