Manuscript VII-B@1 · VII-B.tex · section · be632835

Smooth-edge approximation

Two precise repairs and their limitations › Smooth-edge approximation · lines 1051–1068

VII-B@1#eq:smooth-edge

Choose a smooth function $χ : R \to [0, 1]$ such that

χ (s) = 0 (s \leq 0), χ (s) = 1 (s \geq 1),

and set

θ_{ϵ} (t) = χ (t / ϵ), ϵ > 0.

Define

L_{ϵ} h = E_{R} (θ_{ϵ} C h), q_{a, ϵ} = C^{*} (θ_{ϵ} E_{A} a) .

Displayed formulas in this passage

VII-B@1#eq:smooth-edge · line 1063
$L_{ϵ} h = E_{R} (θ_{ϵ} C h), q_{a, ϵ} = C^{*} (θ_{ϵ} E_{A} a) .$
unlabeled · line 1054
$χ (s) = 0 (s \leq 0), χ (s) = 1 (s \geq 1),$
unlabeled · line 1059
$θ_{ϵ} (t) = χ (t / ϵ), ϵ > 0.$