Towards optimal use of multi-precision arithmetic : a remark

Abstract

If standard-precision computations do not lead to the desired accuracy, then it is reasonable to increase precision until we reach this accuracy. What is the optimal way of increasing precision? One possibility is to choose a constant q > 1, so that if the precision which requires the time t did not lead to a success, we select the next precision that requires time q ̇ ṫ It was shown that among such strategies, the optimal (worst-case) overhead is attained when q = 2. In this paper, we show that this "time-doubling" strategy is optimal among all possible strategies, not only among the ones in which we always increase time by a constant q > 1. © Springer 2006.