the aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. the method is a combination of the asymptotic expansion technique and the reproducing kernel method (rkm). first an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. then the reduced regular delayed diffe...

Description: Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material, greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and explaining when and why these spaces are efficacious. The novel viewpoint is that reproducing kernel Hilbert space theory studies extrinsic geome...

Kernel function, which allows the formulation of nonlinear variants of any algorithm that can be cast in terms of dot products, makes the Support Vector Machines (SVM) have been successfully applied in many fields, e.g. classification and regression. The importance of kernel has motivated many studies on its composition. It’s well-known that reproducing kernel (R.K) is a useful kernel function ...

During the support period July 1, 2011 June 30, 2012, seven research papers were published. They consist of three types: • Research that directly addresses the kernel selection problem in machine learning [1, 2]. • Research that closely relates to the fundamental issues of the proposed research of this grant [3, 4, 5, 6]. • Research that is in the general context of computational mathematics [7...

Kernels between ensembles (or a collection of entities) have recently attracted growing interests in the literature on machine learning . In this paper, we focus on the ‘ensemble’ that is defined as a collection of vectors. One natural way to interpret such an ensemble is through the notion of matrix. We present two basic reproducing kernels between matrices: namely trace and determinant kernel...

In this paper we are concerned with reproducing kernel Hilbert spaces HK of functions from an input space into a Hilbert space Y , an environment appropriate for multi-task learning. The reproducing kernel K associated to HK has its values as operators on Y . Our primary goal here is to derive conditions which ensure that the kernel K is universal. This means that on every compact subset of the...

In this paper we are concerned with reproducing kernel Hilbert spaces HK of functions from an input space into a Hilbert space Y, an environment appropriate for multi-task learning. The reproducing kernel K associated to HK has its values as operators on Y. Our primary goal here is to derive conditions which ensure that the kernel K is universal. This means that on every compact subset of the i...

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.