Abstract— In this paper we represent a parallel implementation of three simultaneous methods for finding the roots of polynomials. We have chosen two well-known simultaneous methods, Durand-Kerner and Ehrich-Aberth and a third new improvement in an asynchronous cluster with 9 processors. We have analysed the time of execution (= time of communication + time of computation) of these algorithms on polynomials with different powers (up to 200) and using different number of processors. For each of these methods we have we have calculated the speed-up. The numerical tests show the global convergence of these methods and through these tests we come into the conclusions when the parallelization is more effective. Some numerical tests are related to the case of using Estrin’s scheme in the evaluation of the polynomials, which gives interesting results in the cases when the polynomial degree is a power of 2.

Index Terms—Speed-up, simultaneous methods, polynomial, parallel implementation.

Eglantina Kalluci, Fatmir Hoxha are with Faculty of Natural Sciences, Department of Applied Mathematics, University of Tirana, Albania (email: eglantina.kalluci@fshn.edu.al, fatmir.hoxha@fshn.edu.al).
Brikena Preni is with Faculty of Mathematical and Physical Engineering, Polytechnic University of Tirana, Albania.

Cite: Eglantina Kalluci, Fatmir Hoxha, Brikena Preni, "The Parallel Implementation of Simultaneous Methods for Finding the Polynomial Zeros," International Journal of Applied Physics and Mathematics vol. 9, no. 2, pp. 111-118, 2019.