Description Usage Format Details Examples

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

1 | ```
data("SobolevKernel")
``` |

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.

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.

1 |

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