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In this paper a one parameter family of one-point iteration formulae for solution of a single variable equation is presented. The formulae are derived on the basis of one-point approximation by the four parameter function . The family includes the Halley's, Chebyshev's and Cauchy's formulae, and, as a limiting case, Newton's formula. All formulae of the family are cubically convergent to simple roots (except Newton's which is quadratically convergent).
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