<![CDATA[We discuss two modications of Newton's methods for solving a nonlinear equation, constructed from two known third-order iterative methods. Our approach is to approximate a derivative from the improvement of the two known third-order iterative methods. Analytically it is shown that each modication of Newton's methodhas third order of convergence, and it requires three function evaluations per iteration. Therefore, its eciency index is 1:414, which is the same as Newton's method. Numerical examples show both methods are competitive with known third-order methods.]]>
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