SobolevKernel: An example of Sobolev kernel

In ardeeshany/FLAME: FLAME for high-dimensional Function-on-Scalar regression problems

Description

Eigenvalues, eigenfunctions (with derivatives) of a Sobolev kernel on the domain D = [0,1] with smoothness parameter σ = 8.

Usage

data("SobolevKernel")

Format

A set of variables associated to the Sobolev kernel

eigenval

vector. J-dimensional vector of the first J eigenvalues of the kernel.

eigenvect

matrix. m \times J matrix of the evaluation of the J eigenfunctions on the time domain seq(0, 1, length = m), where m = 50.

derivatives

matrix. (m-1) \times J matrix of the punctual evaluation of the derivatives of the J eigenfunctions.

Details

The parameter J is selected such that:

∑_{j=1}^J θ_j ≥q \textrm{thres} ∑_{j=1}^∞ θ_j.

with thres in this case equal to 0.99.

Examples

data(SobolevKernel)

ardeeshany/FLAME documentation built on May 14, 2019, 8:41 a.m.