B样条拟插值算子的逼近

Approximation of quasi-interpolation operator by B-spline

研究了以拟插值算子作为工具,针对m阶B样条能表示任意m-1次多项式,利用最小二乘法的向量表示,并依据推导出来的wj(f)的组合形式,利用B样条基函数构造在非均匀节点下的高次拟插值算子作为工具,获得Jackon型估计.

In this paper,the interpolation operator is used as a tool, aiming at m-order B-spline energy which can represent any m-1 order polynomial. Besides,the least square method is employed to represent vector and based on the deduced combination of the,the B-spline basis function is used to construct the high-order interpolation operator under non-uniform node as a tool,finally to get Jackon-type estimate..