Some iterations for factoring a polynomial. II a generalization of the secant method

Abstract

This paper describes an iterative method for factoring a polymonial that bears the same relation to Bairstow's method as the secant method in a single variable bears to Newton's method. Like the secant method, the generalized secant method requires only one function evaluation for each iteration, and like the secant method it converges to a simple factor with order $${{\left( {1 + \sqrt 5 } \right)} \mathord{\left/ {\vphantom {{\left( {1 + \sqrt 5 } \right)} 2}} \right. \kern-\nulldelimiterspace} 2}$$ .