There is no “Uspensky's method.”

Abstract

In this paper an attempt is made to correct the misconception of several authors [1] that there exists a method by Upensky (based on Vincent's theorem) for the isolation of the real roots of a polynomial equation with rational coefficients. Despite Uspensky's claim, in the preface of his book [2], that he invented this method, we show that what Upensky actually did was to take Vincent's method and double its computing time. Upensky must not have understood Vincent's method probably because he was not aware of Budan's theorem [3]. In view of the above, it is historically incorrect to attribute Vincent's method to Upensky.