Newton-like methods and polynomiographic visualization of modified Thakur processes

Abstract

The content of this paper is twofold. First, it aims to provide some new Newton-like methods for solving the root-finding problem in the complex plane. Moreover a convergence test for the resulted methods is phrased and proved. The pseudo-Newton method of Kalantari for finding the maximum modulus of complex polynomials arises as particular case of the newly proposed procedures. Secondly, a recently introduced Thakur iterative process is used in connection with the newly described methods. Its stability and data dependence is subject to analysis. Ultimately, an illustrative analysis regarding some modified Thakur iteration procedures, is obtained via polynomiographic techniques.

Keywords:

• Iterative process
• root-finding algorithm
• polynomiography
• Newton's method
• simulation

2010 Mathematics Subject Classifications:

• 47H09
• 47J05
• 47J25

Disclosure statement

No potential conflict of interest was reported by the author(s).