We examine the convergence properties of a modified Newton-Raphson root method, by using a simple complex polynomial equation, as a test example. In particular, we numerically investigate how a parameter, entering the iterative scheme, affects the efficiency and the speed of the method. Color-coded polynomiographs are deployed for presenting the regions of convergence, as well as the fractality degree of the complex plane. We demonstrate that the behavior of the modified Newton-Raphson method is correlated with the numerical value of the parameter 1. Additionally, there are cases for which the method works flawlessly, while in some other cases we encounter the phenomena of ill-convergence or even non-convergence.
Zotos, Euaggelo E. and Chen, Wei
Exploring the Convergence Properties of a New Modified Newton-Raphson Root Method,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 15,
1, Article 36.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss1/36