Description Usage Arguments Details Value Examples
View source: R/sobolev_kernel_generation.R
Definition of the eigenfunctions and eigenvalues of the kernel for the Sobolev Space H^1((a,b)).
1 | sobolev_kernel_generation(a, b, m, sigma, plot.eigen = FALSE)
|
a |
scalar. left end point of the domain. |
b |
scalar. right end point of the domain. |
m |
scalar, integer. number of points of the interval domain. |
sigma |
scalar. weight σ associated to the derivative in the norm associated to the kernel. See Details for the explicit definition of the norm. |
plot.eigen |
bool. if |
The norm associated to the Sobolev kernel, dependent on the smoothing parameter σ is
\|f\|^2 = \|f\|^2_{L^2} + 1/σ \|f^{\prime}\|^2_{L^2}
The function sobolev_kernel_generation
is implicitly called in the generation_kernel
function when type
parameter is 'sobolev'
. See the Vignette for
the explicit definition of the kernel.
list containing
vectors
matrix. m
\times m
matrix containing
the eigenvectors of the kernel. Each column contains the evaluation of an
eigenfunction on the domain seq(a, b, length = m)
.
values
vector. m
length vector containing the eigenvalues
of the kernel
1 2 | sobolev_kernel_generation(a = 0, b = 1, m = 100,
sigma = 1, plot.eigen = FALSE)
|
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