ﻻ يوجد ملخص باللغة العربية
In this paper we study $L_2$-norm sampling discretization and sampling recovery of complex-valued functions in RKHS on $D subset R^d$ based on random function samples. We only assume the finite trace of the kernel (Hilbert-Schmidt embedding into $L_2$) and provide several concrete estimates with precise constants for the corresponding worst-case errors. In general, our analysis does not need any additional assumptions and also includes the case of non-Mercer kernels and also non-separable RKHS. The fail probability is controlled and decays polynomially in $n$, the number of samples. Under the mild additional assumption of separability we observe improved rates of convergence related to the decay of the singular values. Our main tool is a spectral norm concentration inequality for infinite complex random matrices with independent rows complementing earlier results by Rudelson, Mendelson, Pajor, Oliveira and Rauhut.
We study the recovery of multivariate functions from reproducing kernel Hilbert spaces in the uniform norm. Our main interest is to obtain preasymptotic estimates for the corresponding sampling numbers. We obtain results in terms of the decay of rela
We tensorize the Faber spline system from [14] to prove sequence space isomorphisms for multivariate function spaces with higher mixed regularity. The respective basis coefficients are local linear combinations of discrete function values similar as
We consider the problem of reconstructing an unknown function $uin L^2(D,mu)$ from its evaluations at given sampling points $x^1,dots,x^min D$, where $Dsubset mathbb R^d$ is a general domain and $mu$ a probability measure. The approximation is picked
This paper is devoted to the question of constructing a higher order Faber spline basis for the sampling discretization of functions with higher regularity than Lipschitz. The basis constructed in this paper has similar properties as the piecewise li
By improving the trace finite element method, we developed another higher-order trace finite element method by integrating on the surface with exact geometry description. This method restricts the finite element space on the volume mesh to the surfac