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Exploring The Convergence Properties Of A New Modified Newton-Raphson Root Method, Euaggelo E. Zotos, Wei Chen
Exploring The Convergence Properties Of A New Modified Newton-Raphson Root Method, Euaggelo E. Zotos, Wei Chen
Applications and Applied Mathematics: An International Journal (AAM)
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 …