On an optimal interpolation formula in K_2(P_2) space
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The paper is devoted to the construction of an optimal interpolation formula in K_2(P_2) Hilbert space. Here the interpolation formula consists of a linear combination ∑_β=0^NC_β(z)φ(x_β) of given values of a function φ from the space K_2(P_2). 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. We obtain the optimal interpolation formula by minimizing the norm of the error functional by coefficients C_β(z) of the interpolation formula. The obtained optimal interpolation formula is exact for trigonometric functions sinω x and cosω x. At the end of the paper, we give some numerical results which confirm our theoretical results.
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