光滑函数的Sobolev—Weiner类利用重取样的最优回复

OPTIMAL RECOVERY OF SOBOLEV-WEINER CLASS OF SMOOTH FUNCTIONS BY k-FOLD SAMPLING

讨论定义在全实数轴上的光滑函数的Sobolev-Weiner类利用重取样的最优回复问题.对于二重取样算出了最小信息直径和最小本性误差的精确值,找出了一个最优取样点列并且构造出一个线性最优算法.

An optimal interpolation problem is considered on a Sobolev-Weiner class of smooth functions defined on the real line by k-fold samples. For double samples the exact value of the minimal diameter of information and the minimal intrinsic error are calculated. An optimal set of sampling points is identified. An optimal linear estimator is also constructed.