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Construction of higher-order two-point and globally convergent methods for computing simple roots of nonlinear equations is one of the earliest and challenging problem of numerical analysis. The principle aim of this manuscript is to propose a new highly efficient two-point family of iterative methods having sixth-order convergence, permitting ƒ′(x) = 0, in the vicinity of the required root. Each...
Based on quadratically convergent Schröder’s method, we derive many new interesting families of fourth-order multipoint iterative methods without memory for obtaining simple roots of nonlinear equations by using the weight function approach. The classical King’s family of fourth-order methods and Traub-Ostrowski’s method are obtained as special cases. According to the Kung-Traub conjecture, these...
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