An Exponential-Trigonometric Optimal Interpolation Formula
Abstract
The paper is devoted to derivation of the optimal interpolation formula in Hilbert space $$W_{2}^{(3,0)}(0,1)$$ by Sobolev method. Here the interpolation formula consists of a linear combination of the given values of a function $$\varphi$$ from the space $$W_{2}^{(3,0)}(0,1)$$ . The difference between functions and the interpolation formula is considered as a linear functional called the error functional. The error of the interpolation formula is estimated by the norm of the error functional. It is obtained the optimal interpolation formula by minimizing the norm of the error functional by coefficients of the interpolation formula. The obtained optimal interpolation formula is exact for exponentional-trigonometric functions. At the end of the paper it is given some numerical results, which confirm the numerical convergence of the optimal interpolation formula.