A modified Newton-like method for nonlinear equations

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In this paper, a modified Newton-like method for nonlinear equations is proposed, which is based on a rational model. In the rational model, the Jacobian matrix is approximated by a matrix $$D_{k}$$ which satisfies a new quasi-Newton equation. The new quasi-Newton equation exploits addition information by assuming a quadratic relationship between the information from the last three iterations. Under mild assumptions, the local convergence properties of the new method is presented. Numerical results illustrate that the modified Newton-like method is efficient.