Solution of Equations by Interpolation

Abstract

The present paper deals with the numerical solution of equations by the combined use of Newton's method and inverse interpolation. In Part I the case of one equation in one unknown is discussed. The methods described here were developed by Aitken [1] and Neville [2], but do not seem as widely known as they should be, perhaps because the original papers are not readily available. (A short summary of Aitken's work will be found in a recent paper by Womersley [3].) Mention should also be made of an interesting paper by Spoerl [4], which treats the same problem from a somewhat different viewpoint. In Part II these methods are extended to sets of simultaneous equations.