Optimal interpolation formulas in the periodic function space of S.L. Sobolev
This work provides theoretical foundations for optimal interpolation in a specific function space, but is incremental as it extends known methods to a periodic setting.
The authors derive explicit coefficients for optimal interpolation formulas in the periodic Sobolev space and compute the norm of the error functional, showing a connection to optimal quadrature formulas. Numerical results are provided.
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.