Fast Discrete Fourier Transform on Generalized Sparse Grids
Fast Discrete Fourier Transform on Generalized Sparse Grids
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DOI：
10.1007/978-3-319-04537-5_4
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发表时间：
2014
期刊：
影响因子：
3.2
通讯作者：
M. Griebel;J. Hamaekers
中科院分区：
文献类型：
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作者：
M. Griebel;J. Hamaekers
本文给出了广义稀疏网格上多元函数三角插值的一个算法，并研究了它在控制混合光滑的周期Sobolev空间中函数逼近的应用。特别是，我们得到的误差和成本的估计。我们构造插值的计算成本的复杂性，这是大大低于标准的全网格的情况下。相关的广义稀疏网格插值具有相同的逼近阶为标准的全网格插值，提供了某些额外的正则性假设所考虑的功能得到满足。数值结果验证了我们的理论研究结果。
In this paper, we present an algorithm for trigonometric interpolation of multivariate functions on generalized sparse grids and study its application for the approximation of functions in periodic Sobolev spaces of dominating mixed smoothness. In particular, we derive estimates for the error and the cost. We construct interpolants with a computational cost complexity which is substantially lower than for the standard full grid case. The associated generalized sparse grid interpolants have the same approximation order as the standard full grid interpolants, provided that certain additional regularity assumptions on the considered functions are fulfilled. Numerical results validate our theoretical findings.