Optimal Recovery for Some Infinitely Differentiable Periodic Functions
We determine the optimal convergence rate of Dirichlet interpolating algorithm. Asymptotic inequalities are found for the upper bounds of approximation by trigonometric interpolation on the classes of convolutions of periodic functions admitting regular. The optimal order of m-th minimum linear intrinsic error is determined. By means of previous results about n-widths, we discuss the optimality of interpolation method.
Helen Zhang and David Jin
P. X. Ye and X. H. Li, "Optimal Recovery for Some Infinitely Differentiable Periodic Functions", Advanced Materials Research, Vols. 282-283, pp. 240-243, 2011