Coefficients of Optimal Interpolation Formulas in the Hilbert Space of Differentiable Functions

In this work, we consider the problem of constructing optimal interpolation formulas and we get such formulas that are exact to trigonometric functions $$\sin(\omega x)$$ and $$\cos(\omega x)$$ , and algebraic polynomials of degree $$(m-3)$$ in the Hilbert space of differentiable functions. We obtain analytic formulas for the coefficients of the optimal interpolations formulas. In addition, we consider the problem of restoring curves given by parametric equations in the plane using optimal interpolation formulas.