Reproducing kernel
The Combined Reproducing Kernel Method and Taylor Series for Handling Fractional Differential Equations
... We find the approximate solution by the pro- posed method for n = 2. The absolute er- rors obtained by reproducing Kernel in space W 6 [0, 1], W 7 [0, 1], W 8 [0, 1] are shown in Table 1. This is an ...
10
Discrete Reproducing Kernel Hilbert Spaces: Sampling and Distribution of Dirac-masses
... We study reproducing kernels, and associated reproducing kernel Hilbert spaces (RKHSs) H over infinite, discrete and countable sets V . In this setting we analyze in detail the distributions of the ...
36
On 2-Inner Product Spaces and Reproducing Kernel Property
... In this section, we try to extend the concept of reproducing kernel to 2-inner product spaces. This extension is along with the previews concepts. The main goal of this extension is to construct a new space ...
8
Generalisations of Pick's theorem to reproducing Kernel Hilbert spaces
... In 1964 Laurent Schwartz showed that such a link does indeed exist[Sch64], pro- vided we restrict ourselves to Hermitian kernels that are the difference of two positive kernels. Schwartz’s brilliant paper in fact does ...
120
A computational method for solving weakly singular Fredholm integral equation in reproducing kernel spaces
... In the present paper, we propose a method to solve a class of weakly singular Fredholm integral equations of the second kind in reproducing ker- nel spaces. The Taylor series of the unknown function is used to ...
18
Step Size Adaptation in Reproducing Kernel Hilbert Space
... in reproducing kernel Hilbert space (RKHS) and translate SMD to the nonparametric setting, where its gradient trace parameter is no longer a coefficient vector but an element of the ...
27
A New Approach for Solving Volterra Integral Equations Using The Reproducing Kernel Method
... the reproducing kernel which applied more and more for solving vari- ous problems such as ordinary differential equa- tions, partial differential equations, differential- difference equations, integral ...
6
Chebyshev reproducing kernel method: application to two point boundary value problems
... on reproducing kernel theory, reproducing ker- nels with polynomial form will be constructed and a computational method is described in order to obtain the accurate numerical solution with polynomial ...
19
On Quantile Regression in Reproducing Kernel Hilbert Spaces with the Data Sparsity Constraint
... a Reproducing Kernel Hilbert Space (RKHS) has a similar ...for kernel functions in the RKHS representation has not been carefully studied in the ...the kernel function coefficients to achieve ...
45
New Implementation of Reproducing Kernel Method for Solving Functional Differential Equations
... 2009 Solving Singular Second Order Three-Point Boundary Value Problems Using Reproducing Kernel Hilbert Space Method.. 2012 A Numerical Solution to Nonlinear Second Order Three-Point Bou[r] ...
8
Reproducing Kernel Hilbert space regression with notes on the Wasserstein Distance
... a reproducing-kernel Hilbert space (RKHS) has been extensively studied (Smale and Zhou, 2007; Caponnetto and de Vito, 2007; Steinwart and Christmann, 2008; Mendelson and Neeman, 2010; Steinwart et ...
275
The reproducing kernel thesis for lower bounds of weighted composition operators
... The reproducing kernel thesis is a term com- monly used to describe a body of results that assert that the boundedness of various operators on function spaces such as the Hardy and Bergman space can be ...
9
Model-free Variable Selection in Reproducing Kernel Hilbert Space
... Variable selection is popular in high-dimensional data analysis to identify the truly informa- tive variables. Many variable selection methods have been developed under various model assumptions. Whereas success has been ...
24
Dimensionality Reduction for Supervised Learning with Reproducing Kernel Hilbert Spaces
... We propose a novel method of dimensionality reduction for supervised learning problems. Given a regression or classification problem in which we wish to predict a response variable Y from an explanatory variable X, we ...
27
On weights which admit the reproducing kernel of Bergman type
... In this paper we consider 1 the weights of integration for which the reproducing kernel of the Bergman type can be defined, i.e., the admissible weights, and 2 the kernels defined by suc[r] ...
14
A Brief Digest on Reproducing Kernel Hilbert Space
... the reproducing Hilbert space and showing that if is an RKHS then it has a reproducing ...a kernel to the corresponding RKHS, and the goal is that given a kernel K , we want to construct an ...
5
Learning in reproducing kernel Kreın spaces
... the kernel matrix (C LIP , S HIFT , S QUARE ...indefinite kernel matrix or a spectral trans- formation in place the matrix ...ducing kernel Kre˘ın space is effective, we perform a series of ...
13
Reproducing Kernel Banach Spaces for Machine Learning
... the reproducing kernel for a general RKBS can be an arbitrary function on X ×X ...for reproducing kernels of RKBS to have desired properties as those of RKHS, we may need to impose certain structures ...
35
Gradient descent approach to approximation in reproducing kernel Hilbert spaces
... The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item.. Where records identify the[r] ...
21
Kernel Partial Least Squares Regression in Reproducing Kernel Hilbert Space
... Classical PCR, PLS and RR techniques are well known shrinkage estimators designed to deal with multicollinearity (see, e.g., Frank and Friedman, 1993, Montgomery and Peck, 1992, Jolliffe, 1986). The multicollinearity or ...
27