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Some Modified Newton-Type Methods with Order of Convergence Varied from Two to Six under Weak Conditions

We present some modified Newton-type methods for solving nonlinear equations. These algorithms are free from second derivatives and permit f'(x) = 0 in some iteration points. The convergent analysis demonstrates that the order of convergence and the efficiency index of the present methods are better than that of the classical Newton's method. Some numerical examples are given to illustrate their efficiency and performance.