论文标题
在$ k_2（p_2）$ space的最佳插值公式上
On an optimal interpolation formula in $K_2(P_2)$ space
论文作者
论文摘要
该论文致力于建造$ k_2（P_2）$ HILBERT SPACE中的最佳插值公式。这里的插值公式由一个线性组合$ \ sum_ {β= 0}^nc_β（z）φ（x_β）$（x_β）$ a function $ k_2（p_2）$的函数$φ$的给定值。功能和插值公式之间的差异被认为是一种线性函数，称为误差函数。插值公式的误差由误差函数的规范估计。我们通过将插值公式的$c_β（z）$最小化误差函数的规范来获得最佳的插值公式。获得的最佳插值公式对于三角函数$ \sinΩx$和$ \cosωx$是精确的。在本文的最后，我们给出了一些数值结果，以证实我们的理论结果。
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 $\sum_{β=0}^NC_β(z)φ(x_β)$ 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 $\sinωx$ and $\cosωx$. At the end of the paper, we give some numerical results which confirm our theoretical results.
