Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Jun-Seop Song
Pages: [5] - [18]
Received Date: April 8, 2015
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121485
The purpose of this paper is to present three new methods for finding all simple zeros of polynomials simultaneously. First, we give a new method for finding simultaneously all simple zeros of polynomials constructed by applying the Weierstrass method to the zero in the trapezoidal Newton’s method, and prove the convergence of the method. We also present two modified Newton’s methods combined with the derivative-free method, which are constructed by applying the derivative-free method to the zero in the trapezoidal Newton’s method and the midpoint Newton’s method, respectively. Finally, we give a numerical comparison between various simultaneous methods for finding zeros of a polynomial
polynomial zeros, simultaneous methods, Weierstrass method, convergence, Newton’s method.
