Digit-by-Digit Methods for Polynomials

This paper presents a general system configuration for an arithmetic unit of a computer, which is used to solve polynomial problems efficiently. The technique is based on a digit-by-digit computation of the coefficients of the given polynomial, after the origin has been displaced systematically. Compared with standard techniques, the new scheme, closely allied with Horner's method, is similar in efficiency for polynomial evaluation and is superior for locating roots. The fact that the computed coefficients are related to the derivatives permits the systematic location of all real roots of a real polynomial.