USING THE ARGUMENT PRINCIPLE IN A PROXIMITY TEST FOR ZEROS OF REAL POLYNOMIALS

摘要

In this paper a technique for testing a given circle for zeros of a given real polynomial is presented. The test technique consists of an algorithm for the numerical evaluation of the argument principle. Using this algorithm the exact number of zeros, including multiplicities, possessed by any real polynomial in the unit circle may be determined. After casting the argument principle in terms of Cauchy indices, a Sturm sequence of Chebyshev polynomials, whose length is at most half the degree of the given polynomial, is constructed to determine these indices. The method is found to compare favorably with the Schur-Cohn test.