PlateauExperiment

Compute a vector of K elements containing

\[\frac{1}{j\pi}\int_0^{j\pi} \frac{sin(t)}{t}dt\]

for $1 \leq j \leq K$ by using Taylor Models integration for $[\pi, j\pi]$.

Build a Matrix of Balls representig Convolution with Gaussian Noise of variance σ Galerkin truncated at frequence K

Build a Matrix of Intervals representig Convolution with Gaussian Noise of variance σ Galerkin truncated at frequence K

Plateau map on [0, 1]

Plateau map on [-1, 1]

Compute Pv-v

Convert a matrix of Complex{Interval} to a BallMatrix with a center matrix of complex numbers

Symmetrize density

L2-norm of log(|T'|).

This can be computed explictly as

$\Upsilon(\alpha, \beta) = \sqrt{2}((\ln((1+\beta)\alpha)-(\alpha-1))^2+(\alpha-1)^2)^{\frac{1}{2}}$

Coordinate change from [-1,1] to [0,1]

Coordinate change from [0,1] to [-1,1]