Zobrazeno 1 - 10
of 77
pro vyhledávání: '"Hubbert, Simon"'
This work provides theoretical foundations for kernel methods in the hyperspherical context. Specifically, we characterise the native spaces (reproducing kernel Hilbert spaces) and the Sobolev spaces associated with kernels defined over hyperspheres.
Externí odkaz:
http://arxiv.org/abs/2211.09196
We consider the problem of approximating $[0,1]^{d}$-periodic functions by convolution with a scaled Gaussian kernel. We start by establishing convergence rates to functions from periodic Sobolev spaces and we show that the saturation rate is $O(h^{2
Externí odkaz:
http://arxiv.org/abs/2202.12658
Autor:
Hubbert, Simon, Jäger, Janin
In this paper we compute the spherical Fourier expansions coefficients for the restriction of the generalised Wendland functions from $d-$dimensional Euclidean space to the (d-1)-dimensional unit sphere. The development required to derive these coeff
Externí odkaz:
http://arxiv.org/abs/2110.09835
Publikováno v:
In Applied and Computational Harmonic Analysis January 2023 62:453-474
Autor:
Hubbert, Simon, Levesley, Jeremy
It is well-known that polynomial reproduction is not possible when approximating with Gaussian kernels. Quasi-interpolation schemes have been developed which use a finite number of Gaussians at different scales, which then reproduce polynomials of lo
Externí odkaz:
http://arxiv.org/abs/1711.10803
Autor:
Hubbert, Simon, Levesley, Jeremy
In this paper we present a new multilevel quasi-interpolation algorithm for smooth periodic functions using scaled Gaussians as basis functions. Recent research in this area has focussed upon implementations using basis function with finite smoothnes
Externí odkaz:
http://arxiv.org/abs/1609.02457
Autor:
Bejancu, Aurelian, Hubbert, Simon
The usual power function error estimates do not capture the true order of uniform accuracy for thin plate spline interpolation to smooth data functions in one variable. In this paper we propose a new type of power function and we show, through numeri
Externí odkaz:
http://arxiv.org/abs/1107.4191