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Family of cubically convergent schemes using inverse Newton function for multiple roots. (English) Zbl 1142.65042

Summary: A family of cubically convergent schemes for solving nonlinear equations with multiple roots are proposed. The proposed family is derived from a family of cubically convergent schemes for simple roots based on the inverse Newton function. One function value and two first derivative values are required to be evaluated per iteration and hence, the efficiency of the proposed family is slightly better than that of the classical Newton’s method and the same as that of the most efficient scheme among all the existing methods.

MSC:

65H05 Numerical computation of solutions to single equations
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