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Some eighth-order root-finding three-step methods. (English) Zbl 1221.65115

Summary: We present an improvement of the local order of convergence to increase the efficiency of some fourth-order iterative methods and the order can be improved from four to eight. Per iteration the present methods require three evaluations of the function and one evaluation of its first derivative and therefore have the efficiency index equal to 1.682. Numerical tests verifying the theory are given.

MSC:

65H05 Numerical computation of solutions to single equations
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