Abstract

TERAN-TARAPUES, Juneth Andrea  and  RUA-ALVAREZ, Catalina María. NEWTON’S METHOD FOR COMPLEX ROOTS. FRACTALS IN CAYLEY’S PROBLEM. Rev.EIA.Esc.Ing.Antioq [online]. 2018, vol.15, n.29, pp.97-108. ISSN 1794-1237.  https://doi.org/10.24050/reia.v15i29.1131.

When the search for the solution of an application problem involves the resolution of nonlinear equations, numerical methods are used. Newton’s method is one of the most used because of its versatility and agility and due to this is an excellent option to approximate the solutions of non-linear equation systems. Solving equations with complex variable through Newton’s method has an interesting application in the field of fractals such as Cayley’s problem and the fractal figures produced by the convergence, divergence and efficiency of the method. In this paper the study of the Cayley’s problem is presented through the generalization of Newton’s method to 2. In addition, are presented some fractal produced by iterations of the Newton’s method in the complex plane.

Keywords : Newton’s method; Non-linear equation system; Complex roots; Cayley’s problem; Fractal.

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