改造的Catmull-Rom插值基函数及其逼近性质

Remould Catmull-Rom interpolation basis functions and approximative properties

此文利用多项式再生性和局部支撑性对著名的Catmull-Rom插值基函数进行改造,获得新的插值基函数,生成新的插值算子,并求得新插值算子精确的Lebesgue常数,估计了其逼近连续函数的收敛速度,理论和数值例子都表明新插值算子的逼近效果优于其他各类插值算子.

The paper utilizes polynomial reproducibility and local support to modify the famous Catmull Rom interpolation basis function,obtaining new interpolation basis functions,generating new interpolation operators,and also obtaining the precise Lebesgue constant of the new interpolation operator.The convergence speed of the new interpolation operator approaching continuous functions is estimated,and both theoretical and numerical examples show that the approximation effect of the new interpolation operator is better than other types of interpolation operators.