New and Efficient Program for Finding all Polynomial Roots.

摘要

Finding polynomial roots rapidly and accurately is an important problem in many areas of signal processing. We present a new program which is a combination of Muller's and Newton's method. We use the former for computing a root of the deflated polynomial which is a good estimate for the root of the original polynomial. This estimate is improved by applying Newton's method to the original polynomial. Furthermore we give a simple approach to improve the accuracy for spectral factorization in the case there are double roots on the unit circle. Finally we briefly consider the inverse problem of root finding, i.e. computing the polynomial coefficients from the roots which may lead to surprisingly large numerical errors.