On the improved Newton-like methods for the inclusion of polynomial zeros

Abstract

The aim of this paper is to present some modifications of Newton's type method for the simultaneous inclusion of all simple complex zeros of a polynomial. Using the concept of the R-order of convergence of mutually dependent sequences, the convergence analysis shows that the convergence rate of the basic method is increased from 3 to 6 using Jarratt's corrections. The proposed method possesses a great computational efficiency since the acceleration of convergence is attained with only few additional calculations. Numerical results are given to demonstrate convergence properties of the considered methods.

Keywords:

• zeros of polynomials
• simultaneous methods
• inclusion methods
• circular interval arithmetic
• acceleration of convergence
• computational efficiency

2000 AMS Subject Classifications :

• 65H05
• 65G20
• 30C15

Acknowledgements

This work was supported by the Serbian Ministry of Science under grant 144024.