Superoptimal continued fractions

Abstract

Motivated by the optimal continued fractions studied independently by Selenius and Bosma, we define and introduce algorithms producing superoptimal continued fraction expansions of irrationals. The convergents of these expansions simultaneously provide arbitrarily good rational approximations and converge arbitrarily quickly.

15 pages, 5 figures. Includes new figure (Fig. 4) and other small improvements following referee suggestions. Accepted by Proc. Amer. Math. Soc