We construct approximate Fekete point sets for kernel-based interpolation by maximising the determinant of a kernel Gram matrix obtained via truncation of an orthonormal expansion of the kernel. Uniform error estimates are proved for kernel interpolants at the resulting points. If the kernel is Gaussian, we show that the approximate Fekete points in one dimension are the solution to a convex optimisation problem and that the interpolants converge with a super-exponential rate. Numerical examples are provided for the Gaussian kernel.

中文翻译：

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近似Fekete点的基于核的插值

我们通过最大化通过截取核的正交展开而获得的核Gram矩阵的行列式，来构造基于内核的插值的近似Fekete点集。在结果点上证明了内核插值的均匀误差估计。如果核是高斯，则表明一维近似Fekete点是凸优化问题的解，并且内插值以超指数速率收敛。提供了高斯核的数值示例。