A Stopping Criterion for Polynomial Root Finding When searching for the root of a polynomial, it is generally difficult to know just when to accept a number as an adequate approximation to the root. In this paper an algorithm is presented which allows one to terminate the iteration process on the basis of calculated bounds for the roundoff error which occurs in evaluating the polynomial. This stopping criterion has been tested on numerous examples and has been found to serve as a satisfactory means for accepting a complex number as a zero of a real polynomial. CACM October, 1967 Adams, D. A. CA671009 JB February 27, 1978 1:56 PM 1524 4 1524 1524 4 1524 1524 4 1524 1931 4 1524 2214 4 1524 2544 4 1524 1197 5 1524 1524 5 1524 1524 5 1524 1524 5 1524 311 5 1524 2544 5 1524 879 5 1524 1524 6 1524 311 6 1524 2214 6 1524