In this paper, we prove convergence results for multiscale approximation using compactly supported radial basis functions restricted to the unit sphere, for target functions outside the reproducing kernel Hilbert space of the employed kernel.

We consider reproducing kernel Hilbert spaces of Dirichlet series with kernels of the form k(s, u) = ∑ ann −s−ū, and characterize when such a space is a complete Pick space. We then discuss what it means for two reproducing kernel Hilbert spaces to be “the same”, and introduce a notion of weak isomorphism. Many of the spaces we consider turn out to be weakly isomorphic as reproducing kernel Hil...

The aim of this paper is to use the Reproducing kernel Hilbert Space Method (RKHSM) to solve the linear and nonlinear fuzzy impulsive fractional differential equations. Finding the numerical solutionsof this class of equations are a difficult topic to analyze. In this study, convergence analysis, estimations error and bounds errors are discussed in detail under some hypotheses which provi...

In this paper, we prove convergence results for multiscale approximation using compactly supported radial basis functions restricted to the unit sphere, for target functions outside the reproducing kernel Hilbert space of the employed kernel.

In this paper, a new partition of unity ± the synchronized reproducing kernel (SRK) interpolant ± is derived. It is a class of meshless shape functions that exhibit synchronized convergence phenomenon: the convergence rate of the interpolation error of the higher order derivatives of the shape function can be tuned to be that of the shape function itself. This newly designed synchronized reprod...

We give several properties of the reproducing kernel Hilbert spaces induced by the Gaussian kernel and their implications for recent results in the complexity of the regularized least square algorithm in learning theory.

We focus on covariance criteria for finding a suitable subspace for regression in a reproducing kernel Hilbert space: kernel principal component analysis, kernel partial least squares and kernel canonical correlation analysis, and we demonstrate how this fits within a more general context of subspace regression. For the kernel partial least squares case some variants are considered and the meth...

where (Ω,μ) is a probability space. The kernel K is used to generate a Hilbert space, known as a reproducing kernel Hilbert space, whose unit ball is the class of functions we investigate. Recall that if K is a positive definite function K : Ω×Ω → R, then by Mercer’s Theorem there is an orthonormal basis (φi)i=1 of L2(μ) such that μ× μ almost surely, K(x,y) = ∑i=1 λiφi(x)φi(y), where (λi)i=1 is...

The functional generalized additive model (FGAM), also known as the continuous additive model (CAM), provides a more flexible functional regression model than the well-studied functional linear regression model. This paper restricts attention to the FGAM with identity link and additive errors, which we will call the additive functional model and is a generalization of the functional linear mode...