XII.—Further Numerical Studies in Algebraic Equations and Matrices

Abstract

In a former paper on the same subject the writer pointed out that the sequence used by D. Bernoulli for approximating to the greatest root of an algebraic equation could be further utilised in such a way as to give all the roots. It is suggested in the present paper that there is really no need to compute a first Bernoullian sequence at all, but that by the theory of dual symmetric functions the coefficients in the given equation may be used with equal convenience. In a practical respect this simplifies the technique of root-evaluation.