Efficient parallel rooting of complex polynomials on the unit circle

Abstract

An efficient method is presented for rooting complex polynomial equations of any order where the root space is restricted to the unit circle. The method restates the evaluation of polynomials as a recursive algorithm involving only additions. By means of the bilinear transformation, the straight line, uniformly spaced, recursive polynomials evaluation method of A.H. Nuttall (1987) is extended to the unit circle where the root positions are determined by thresholding. General coefficient transformations are provided along with a comparison to the Horner method. >