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Efficient high-order methods based on golden ratio for nonlinear system

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Applied Mathematics and Computation

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. © 2010 Elsevier Inc. All rights reserved.