Optimal interpolation formulas in the periodic function space of S.L. Sobolev

Abstract: In this paper the problem of construction of lattice optimal interpolation formulas in the space $\widetilde{L_2^{(m)}} (0,1)$ is considered. Using S.L. Sobolev's method explicit formulas for the coefficients of lattice optimal interpolation formulas are given and the norm of the error functional of lattice optimal interpolation formulas is calculated. Moreover, connection between optimal interpolation formula in the space $\widetilde{L_2^{(m)}} (0,1)$ and optimal quadrature formula in this space is shown. Finally, numerical results are given.