A continued fraction algorithm

Abstract

Two existing algorithms for the evaluation of a finite sequence of convergents of a continued fraction are considered. Each method has a drawback concerning numerical stability or computational effort. A third algorithm is presented which requires less computations than the first method, and generally is more stable than the second one. The results are illustrated by numerical examples. The connection with Miklogko's algorithm is shown.

Some Properties of a Third Order Partial Recurrence Relation

“…Here we consider a plausible case for how a generalized continued fraction can be related to arbitrary order sequences. Previous work (for example [14,15]) has tended to focus on going from the continued fraction algorithm to the recurrence relation or difference equation, whereas we are attempting to go in the opposite direction.…”

An a priori estimate for the truncation error of a continued fraction expansion to the Gaussian error function

“…For rounding error analysis, stability and complexity the reader is referred to Olver [18] and van der Cruyssen [3], [25] and [26].…”