OPTIMAL ERROR BOUNDS FOR CUBIC SPLINE INTERPOLATION
OPTIMAL ERROR BOUNDS FOR CUBIC SPLINE INTERPOLATION
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DOI：
10.1016/0021-9045(76)90040-x
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发表时间：
1976-01-01
影响因子：
0.9
通讯作者：
MEYER, WW
中科院分区：
文献类型：
--
作者：
HALL, CA;MEYER, WW
所考虑的误差界限的形式为 ∥f(r)−s(r)∥∞⩽Cr∥f(4)∥∞h4 −r，其中是 ϵC4[a,b] 的三次样条插值，匹配 fin 斜率或在 [a,b] 端点处的二阶导数。通过对早期（1968）分析的细化和扩展，我们获得了常数 C0、C1、C2、C3，它们比迄今为止已知的应用更广泛并且（C0 除外）更小。表明C0和C1无法进一步提高。该参数调用欧拉样条作为极值函数，并导致均匀网格上一般奇数次样条插值的误差界限。
The error bounds considered are of the form ∥f(r)−s(r)∥∞⩽Cr∥f(4)∥∞h4 −r, wheresis a cubic spline interpolant offϵC4[a,b], matchingfin slope or in second derivative at the endpoints of [a,b]. By refinement and extension of an earlier (1968) analysis, we obtain constantsC0,C1,C2,C3, which are more widely applicable and (except forC0) smaller than heretofore known. It is shown thatC0andC1cannot be further improved. The argument invokes the Euler spline as extremal function and leads to an error bound for spline interpolation of general odd degree over a uniform mesh.