The paper is concerned with classic kernel interpolation methods, in addition to approximation methods that are augmented by gradient measurements. To apply kernel interpolation using radial basis functions (RBFs) in a stable way, we propose a type of quasi-optimal interpolation points, searching from a large set of candidate points, using a procedure similar to designing Fekete points or power function maximizing points that use pivot from a Cholesky decomposition. The proposed quasi-optimal points results in smaller condition number, and thus mitigates the instability of the interpolation procedure when the number of points becomes large. Applications to parametric uncertainty quantification are presented, and it is shown that the proposed interpolation method can outperform sparse grid methods in many interesting cases. We also demonstrate the new procedure can be applied to constructing gradient-enhanced Gaussian process emulators.

除了通过梯度测量增强的近似方法外，本文还涉及经典的内核插值方法。为了稳定地使用径向基函数（RBF）应用内核插值，我们提出了一种准最优插值点，从大量候选对象中进行搜索使用与设计Fekete点或幂函数最大化的点类似的过程，这些点使用来自Cholesky分解的枢轴。提出的准最佳点导致条件数较小，因此减轻了点数变大时插值过程的不稳定性。提出了在参数不确定性量化中的应用，并且表明在许多有趣的情况下，所提出的插值方法可以胜过稀疏网格方法。我们还演示了该新过程可用于构建梯度增强的高斯过程仿真器。