Kernel-based interpolation at approximate Fekete points
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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 convergence with a super-exponential rate. A numerical experiment is provided for the Gaussian kernel.
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