Rounding error analysis for forward continued fraction algorithms

AbstractThere exist several algorithms for the calculation of convergents of a continued fraction. We will investigate the effect of data perturbations and rounding errors for some algorithms, using the ideas of Stummel's perturbation theory [3] which is a forward error analysis.In Section 1 we briefly repeat the forward a priori error analysis which we shall use. In Section 2 we present three forward recurrence algorithms (including a method which we believe to be new) and the well-known backward recurrence algorithm for the calculation of a convergent of a given continued fraction. The next four sections are devoted to the a priori error analysis of the four algorithms. The theoretical results are applied to numerical examples in Section 7. As far as the rounding errors were concerned no algorithm was better or worse than the others for all the examples and no error bounds were especially more accurate than the other ones