In this paper, we present a new sixth-order iterative method for solving nonlinear systems\nand prove a local convergence result. The new method requires solving five linear systems per\niteration. An important feature of the new method is that the LU (lower upper, also called\nLU factorization) decomposition of the Jacobian matrix is computed only once in each iteration.\nThe computational efficiency index of the new method is compared to that of some known methods.\nNumerical results are given to show that the convergence behavior of the new method is similar to the\nexisting methods. The new method can be applied to small- and medium-sized nonlinear systems.
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