tex-projects/LaTeX-examples
2
0
Fork 0
mirror of https://github.com/MartinThoma/LaTeX-examples.git synced 2025-04-25 14:28:05 +02:00
Code Activity

added comment 'symmetry axis'

Browse source
This commit is contained in:
Martin Thoma 2013-12-06 00:37:04 +01:00
parent e87bfb42ea
commit f92637625d
1 changed files with 1 additions and 1 deletions
Download patch file Download diff file Expand all files Collapse all files

2
documents/math-minimal-distance-to-cubic-function/math-minimal-distance-to-cubic-function.tex
View file

@ -356,7 +356,7 @@ For all other points $P = (0, w)$, there are exactly two minima $x_{1,2} = \pm \
So the solution is given by So the solution is given by
\begin{align*} \begin{align*}
x_S &:= - \frac{b}{2a}\\ x_S &:= - \frac{b}{2a} \;\;\;\;\; \text{(the symmetry axis)}\\
\underset{x\in\mdr}{\arg \min d_{P,f}(x)} &= \begin{cases} \underset{x\in\mdr}{\arg \min d_{P,f}(x)} &= \begin{cases}
x_1 = +\sqrt{a (y_p + \frac{b^2}{4a} - c) - \frac{1}{2}} + x_S \text{ and } &\text{if } x_P = x_S \text{ and } y_p + \frac{b^2}{4a} - c > \frac{1}{2a} \\ x_1 = +\sqrt{a (y_p + \frac{b^2}{4a} - c) - \frac{1}{2}} + x_S \text{ and } &\text{if } x_P = x_S \text{ and } y_p + \frac{b^2}{4a} - c > \frac{1}{2a} \\
x_2 = -\sqrt{a (y_p + \frac{b^2}{4a} - c) - \frac{1}{2}} + x_S\\ x_2 = -\sqrt{a (y_p + \frac{b^2}{4a} - c) - \frac{1}{2}} + x_S\\