Numerical Investigation into the Mixed Precision GMRES(m) Method Using FP64 and FP32

抄録

In this paper, a mixed precision variant of the GMRES(m) method using FP64 and FP32 is investigated. Through numerical experiments for various test matrices and different settings of the restart frequency m, its numerical behavior is examined in detail and compared with that of the conventional GMRES(m) method using only FP64. From the obtained numerical results, it is confirmed that if a problem is solved by the conventional GMRES(m) method, basically the mixed precision GMRES(m) can also solve it. In addition, in the case of using small m, the number of the total iterations is almost equivalent between the two methods. However, when m grows, a different tendency is observed; the number of the iterations decreases in the conventional methods but increases in the mixed precision method. These results and observations provide new insights of the mixed precision GMRES(m) method, which will be helpful for the efficient use in applications and the further improvement of the method.