Abstract
This chapter presents two fixed point principles. It discusses an iterational process that uses interpolation formulas and allows the calculation of the root of the equation f(x) = 0 in space R1. In each step of this process, a new algebraic equation is constructed, whose order coincides with the order of applied interpolation formula and one of its roots is computed. The sequence of these roots converges to the root of equation, if some assumptions are fulfilled a priori. This chapter presents two fixed point principles in complete metric spaces. The application is adduced to one iterational process in space R1, which is evoked with use of the formulas of inverse interpolation. This iterational process requires only rational operations, and its convergence is proven without any a priori assumptions.
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