论文标题
基于采样的繁殖核函数的近似值
Sampling based approximation of linear functionals in Reproducing Kernel Hilbert Spaces
论文作者
论文摘要
在本文中，我们分析了一种贪婪的程序，以近似通过淋巴结值在繁殖核希尔伯特空间中定义的线性功能。此过程计算一个正交规则，该规则可以应用于一般功能，包括集成功能。对于大量功能，我们通过均匀和贪婪的点来证明近似值的收敛结果，这些点以各种方式概括了几个已知结果。还讨论了权重和节点计算的扰动分析。除了理论研究之外，我们从数字上证明了我们的算法在处理各种整合密度方面有效，并且与现有的不确定性定量方法相比，它甚至非常有竞争力。
In this paper we analyze a greedy procedure to approximate a linear functional defined in a Reproducing Kernel Hilbert Space by nodal values. This procedure computes a quadrature rule which can be applied to general functionals, including integration functionals. For a large class of functionals, we prove convergence results for the approximation by means of uniform and greedy points which generalize in various ways several known results. A perturbation analysis of the weights and node computation is also discussed. Beyond the theoretical investigations, we demonstrate numerically that our algorithm is effective in treating various integration densities, and that it is even very competitive when compared to existing methods for Uncertainty Quantification.
