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

作　　者：刘星 章仁江[1] LIU Xing;ZHANG Ren-jiang(Department of Mathematics,Zhejiang Gongshang University,Hangzhou 310018,China)

机构地区：[1]浙江工商大学统计与数学学院,浙江杭州310018

出　　处：《高校应用数学学报（A辑）》2024年第4期391-403,共13页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：浙江省自然科学基金(LY24F020002)。

摘　　要：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.

关 键 词：插值 连续模 逼近误差 LEBESGUE常数 基函数 

分 类 号：O174[理学—数学]