Generalization and acceleration of an algorithm of Sebastião e Silva and its duals

Abstract

In this paper, we extend Householder's [4] generalization of an algorithm of Sebastião e Silva [11] by adding a new elimination rule for defining the sequences which converge to the factors of the given polynomial. We then present the dual algorithm and show that the dual algorithm becomes equivalent to the direct algorithm in the generalized form. Next, we give accelerated forms of these algorithms which are quadratically convergent. We also study the relation of these methods to other methods.