Multivariate Interpolation with Fundamental Splines of Fractional Order
Multivariate Interpolation with Fundamental Splines of Fractional Order
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具有分数阶基本样条的多元插值
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
P. Massopust
中科院分区：
文献类型：
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作者：
B. Forster;P. Massopust
分数阶B样条Bσ， σ≥1，是插值经典勋伯格样条$B_n， n在{
m I！N}$，关于度。当Schoenberg样条≥3阶时，它们一般不满足插值性质$B_sigma(n-k) = delta_{n,k},n,k in {
m Z!!Z}$。但是，应用插值滤波器$1/sum_{kin{
m Z!！Z}} hat{B}_{σ}(ω -2 π k)$ -如果定义良好-在频域得到满足插值性质的分数阶基本样条。我们通过脊函数将这些结果推广到多元分数B样条。（©2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim）
Fractional B‐splines Bσ, σ ≥ 1, are piecewise polynomials of fractional degree that interpolate the classical Schoenberg splines $B_n, n in {
m I!N}$, with respect to the degree. As the Schoenberg splines of order ≥ 3, they in general do not satisfy the interpolation property $B_sigma(n-k) = delta_{n,k},n,k in {
m Z!!Z}$. However, the application of the interpolation filter $1/sum_{kin{
m Z!!Z}} hat{B}_{sigma}(omega-2 pi k)$—if well‐defined—in the frequency domain yields a fundamental spline of fractional order that does satisfy the interpolation property. We extend these result via ridge functions to multivariate fractional B‐splines. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)