High-order polynomial root tracking algorithm

A new, efficient algorithm for tracking the roots of time-varying polynomials with complex coefficients is presented. The algorithm updates a vector of polynomial roots in response to a perturbation in polynomial coefficients. The update requires only the solution of a single set of linear equations. The algorithm has been used successfully to track the roots of high-order polynomials. The accuracy of the algorithm can be improved by iteration. When operated iteratively, it converges rapidly, and usually requires less than ten iterations to reach the maximum accuracy achievable using sixteen significant digital arithmetic