具有有效低维特性的稀疏网格与高维函数的改进采样不等式
Improved Sampling Inequalities for Sparse Grids and High-Dimensional Functions with Effective Low Dimension
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中文总结 AI 辅助
针对高维函数近似的维度诅咒问题，将稀疏网格与锚定投影技术结合，推导稀疏网格新采样不等式并结合非匹配采样过程的回归方法，得到有效低维 Sobolev 函数的改进采样不等式。
中文摘要 AI 辅助
高维函数的近似因常出现的“维度诅咒”而成为一项挑战性任务。本文将稀疏网格与锚定投影技术结合，针对具有主导混合正则性的有效低维 Sobolev 函数推导采样不等式。为此，我们推导了稀疏网格的新采样不等式，并将其与近期研究的非匹配采样过程的回归方法相结合。
英文摘要
The approximation of high-dimensional functions is a challenging task due to the often appearing curse of dimensionality. In this paper, we combine sparse grid with anchored projection techniques to derive sampling inequalities for Sobolev functions of a dominating mixed regularity which are effectively low dimensional. To this end, we derive new sampling inequalities for sparse grids and combine these with recently investigated regression processes of non-matching sampling processes.
