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. For a large class of functionals, that includes integration functionals and other interesting cases, but does not include differentiation, we prove convergence results for the approximation by means of quasi-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.

在本文中，我们分析了一个贪婪过程，以通过节点值来逼近再现内核希尔伯特空间中定义的线性函数。此过程将计算可应用于通用功能的正交规则。对于一大类函数，其中包括积分函数和其他有趣的情况，但不包括微分，我们通过准均匀点和贪婪点证明了逼近的收敛结果，这些点以各种方式概括了几种已知结果。还讨论了权重的扰动分析和节点计算。除了理论研究之外，我们还在数值上证明了我们的算法可以有效地处理各种积分密度，并且与现有的不确定性量化方法相比，它甚至具有很高的竞争力。