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In this paper, we present a uniparametric family of modified Chebyshev-Halley type methods with optimal eighth-order of convergence. In terms of computational cost, each member of the family requires only four functional evaluations per step, and hence is optimal in the sense of Kung-Traub conjecture. Moreover, in order to have additional information to choose some elements of the class, in particular...
The paper is devoted to description of certain ways of extending the domain of convergence of Newton’s method. This paper is a survey of contributions of representatives of Soviet and Russian mathematical school, namely, Kalitkin, Puzynin, Madorskij and others. They introduced different kinds of damping multiplier and showed that their usage may be helpful and beneficial while solving different nonlinear...
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