| Abstract: | 1. Iteration is an operation with many aspects; we shall here only occupy ourselves with iteration as a means of numerical determination of a real root of an equation. Nor shall we go into the whole of the theory of this subject 2 See, for instance, Whittaker & Robinson: The Calculus of Observations, or Runge & König: Vorlesungen über numerisches Rechnen. , our principal object being to show how the process of iteration which is often futile in its primitive form may be improved by a suitable combination of three consecutive values. But before doing this, it will be convenient to recall briefly some of the principles involved in iteration. |
