ON ZEROS OF A COMPLEX POLYNOMIAL

In the present work the problem of finding the zeros of a polynomial P(x) with complex coefficients is considered. First, all of its real and complex zeros occurring in pairs are computed by finding the zeros of the greatest common divisor of P-Re(x) and P-Im(x) (i.e. sub-polynomials forming real and imaginary part of P(x)). The greatest common divisor of the two polynomials having integer coefficients is obtained by applying Bareiss's integer preserving algorithm using integer arithmetic. In case of real polynomials approximate GCD is obtained by applying the Euclidean algorithm, where polynomial division is performed by applying Routh Array-type division algorithm. The approximate GCD is further improved by performing iterative divison. The complex zeros of the reduced complex polynomial are then obtained by applying the Argument-Principle algorithm. It is observed that the method works well and produces accurate zeros within a specified accuracy.