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In this paper, we present some new third-order iterative methods for finding a simple root α of nonlinear scalar equation f(x)=0 in R. A geometric approach based on the circle of curvature is used to construct the new methods. Analysis of convergence shows that the new methods have third-order convergence, that is, the sequence {xn} 0∞ generated by each of the presented methods converges to α...
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