应用数学2025，Vol.38Issue(2)：446-452,7.
等距剖分下三次样条插值误差的精细估计
A Fining Error Estimation Between the Object Function and Its Cubic Spline Interpolating Function Under Equidistant Partitioning
摘要
Abstract
The interpolating error estimation is considered between the object function and it-s corresponding spline interpolating function.Using Taylor's formula,mean theorem,and the skill of exchanging integration sequence,the moment or the second derivatives difference estimation is firstly in-vestigated at each interpolating node.Based on the prepared work,a fine approximation is further derived for the third-order derivative difference for any object function and its corresponding spline interpolating function.A fine result is obtained if both the object function is C5continuous and the interpolating abscis-sae are equidistantly selected.The leading coefficient C3=1/2 is acquired where appears in the estimated bound expression C3h|f|4,∞,which is superior to the known conclusions.Till now Hall together with Meyer gave C3=1 under uniform partition,and WONG got C3=1+√3/4.关键词
样条插值/误差估计/函数逼近Key words
Spline interpolation/Error estimation/Function approximating分类
数理科学引用本文复制引用
宋士仓,宋晓源,宋舒涵..等距剖分下三次样条插值误差的精细估计[J].应用数学,2025,38(2):446-452,7.基金项目
973项目基金(2012CB025904) （2012CB025904）
