In this paper we propose a new approach for the modelling of the multi-variable systems (MIMO) on the Reproducing Kernel Hilbert Space (RKHS). The proposed approach considers the MIMO system as a set of MISO processes modelled in RKHS space. We propose also a comparative study of three identification kernel methods of nonlinear systems modelled in Reproducing Kernel Hilbert Space (RKHS), where ...

and Applied Analysis 3 2. Several Reproducing Kernel Spaces In this section, several reproducing kernels needed are constructed in order to solve 1.1 and 1.2 using RKHSmethod. Before the construction, we utilize the reproducing kernel concept. Throughout this paper C is the set of complex numbers, L2 a, b {u | ∫b a u2 x dx < ∞}, l2 {A | ∑∞i 1 Ai 2 < ∞}, and the superscript n in u n t denotes th...

We study learning algorithms generated by regularization schemes in reproducing kernel Hilbert spaces associated with an -insensitive pinball loss. This loss function is motivated by the -insensitive loss for support vector regression and the pinball loss for quantile regression. Approximation analysis is conducted for these algorithms by means of a variance-expectation bound when a noise condi...

Given a positive definite, bounded linear operator A on the Hilbert space H0 := l(E), we consider a reproducing kernel Hilbert space H+ with a reproducing kernel A(x, y). Here E is any countable set and A(x, y), x, y ∈ E, is the representation of A w.r.t. the usual basis of H0. Imposing further conditions on the operator A, we also consider another reproducing kernel Hilbert space H − with a ke...

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, we propose a relatively new semi-analytical technique to approximate the solution of nonlinear multi-order fractional differential equations (FDEs). We present some results concerning to the uniqueness of solution of nonlinear multiorder FDEs and discuss the existence of solution for nonlinear multi-order FDEs in reproducing kernel Hilbert space (RKHS). We further give an error a...