On Morimoto Algorithm in Diophantine Approximation
On Morimoto Algorithm in Diophantine Approximation
Let us denote the continued fraction expansion of an irrational number $\alpha(0<\alpha<])$ by $\alpha=[0:e_{1}, e_{2}, \cdots]$ , and its n-th convergent by $p_{n}/q_{n}$ .We call the sequence of partial quotients $\{e_{i} ; i=1,2, \cdots\}$ the name of $\alpha$ associated with the simple continued fraction algorithm.The following theorems are well known.THEOREM …