On the numerical solution of equations with complex roots

Abstract

1. Introduction .-Part I and II of the present paper give a brief description of two methods, which are believed to be substantially novel, for the numerical resolution of equations with complex roots. As regards rapidity of computation, the methods will probably be found inferior to others such as Aitken's extension of Bernoulli's method, or the root-squaring method as improved by Brodetsky and Smeal. On the other hand, a feature of the alternatives proposed is that arithmetical errors need not be cumulative. Certain further merits will be suggested in due course. Part III contains a résumé of Bairstow's variant of the root-squaring method, and Part IV deals with successive approximation to a quadratic factor. The substance of these parts has already appeared in aeronautical pulications, but may not be familiar to the general scientific public.