Abstract
THIS paper presents an iteration procedure for determining isolated simple roots of the equation f( x) = 0 more accurately; particular cases of this are the well-known methods of Newton's tangents [1], of Chebyshev's tangential parabolas [1], of Salekhov's tangential hyperbolas [2], methods based on Koenig's theorem, and others. The convergence of the proposed method is studied, it is proved to be a method of order ( n + 2), the rate of convergence is established and examples are given. The theoretical part of the paper was written by S. A. Kas'yanyuk, and the applied part by V. A. Varyukhin.
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