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Efficient high-order methods based on golden ratio for nonlinear systems |
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| Authors: | Alicia Cordero José L Hueso Eulalia Martínez Juan R Torregrosa |
| Institution: | Instituto de Matemática Multidisciplinar, Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022 Valencia, Spain |
| Abstract: | We derive new iterative methods with order of convergence four or higher, for solving nonlinear systems, by composing iteratively golden ratio methods with a modified Newton’s method. We use different efficiency indices in order to compare the new methods with other ones and present several numerical tests which confirm the theoretical results. |
| Keywords: | Nonlinear systems Newton&rsquo s method Fixed point iteration Convergence order Efficiency indices |
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