On the weierstrass and some petkovic-like methods for numerical determination of polynomial zeros

Abstract

In this paper, we consider the Weierstrass method to present a useful modification which requires no additional information to implement though with some extra computational effort. Acceleration of convergence is made possible by means of the Gauss–Seidel sense of updating the iterates. Further methods are derived by application of the process of hybrid combination with other simultaneous inclusion methods. Some Petkovic-like methods which incorporate automatic determination of the error bounds of the computed zeros without the need for the rigours of disk inversions are also considered. The accuracy of the methods is demonstrated by some numerical examples.

Keywords:

• Polynomials
• Zeros
• Interval arithmetic
• Combination methods
• Convergence