An Acceleration Of The DURAND-KERNER Algorithm Using The Homotopy Method

Finding polynomial roots rapidly and accurately is an important mathematic problem. However, Galois'famous theorem states that the only polynomial equations that possess a general solution in terms of explicit formulas are those of degree not exceeding four. For the computation of zeros of polynomials of higher degree one therefore must resort to numerical methods. Among them, Durand-Kerner algorithm is very famous. But whether the algorithm can converge rapidly or not relies on choosing good initial values. So in this paper, we discuss how to use the homotopy method to get good initial values and accelerate the classic Durand-Kerner algorithm.