Interpolation and Applications

The research contains an elementary treatment of the fundamental concepts concerning interpolation of real functions of one variable, and a few applications of interpolation in solving approximation problems and numerical computation. Approximation methods for the roots of the scalar equations using inverse interpolation are presented and analyzed. There are also analyzed certain iterative methods of interpolation type (some of them optimal, with respect to the number of function evaluations vs the convergence order), both from the point of view of the convergence order and of the efficiency index. We also present some approximation methods for the values of the derivatives of real functions, for the integrals of real functions on finite intervals, for the solutions of boundary value problems for ordinary or partial differential equations. Some results contained in this study are classical and well-known, while some other results are rather new; the later were obtained and then published by the authors, as well as by other authors working in this area of research.