aboutsummaryrefslogtreecommitdiff
path: root/content
diff options
context:
space:
mode:
authorAdrian Kummerlaender2017-02-15 23:06:37 +0100
committerAdrian Kummerlaender2017-02-15 23:06:37 +0100
commit8fb9afb23101c290c6c624bde59a44f2d517f731 (patch)
treeaff07d1a1e6dac293fb32fc21e005a41dd196588 /content
parent27315f8df52f43626c72c4018339172de8797a04 (diff)
downloadmath_reference_sheets-8fb9afb23101c290c6c624bde59a44f2d517f731.tar
math_reference_sheets-8fb9afb23101c290c6c624bde59a44f2d517f731.tar.gz
math_reference_sheets-8fb9afb23101c290c6c624bde59a44f2d517f731.tar.bz2
math_reference_sheets-8fb9afb23101c290c6c624bde59a44f2d517f731.tar.lz
math_reference_sheets-8fb9afb23101c290c6c624bde59a44f2d517f731.tar.xz
math_reference_sheets-8fb9afb23101c290c6c624bde59a44f2d517f731.tar.zst
math_reference_sheets-8fb9afb23101c290c6c624bde59a44f2d517f731.zip
Update README.md
Diffstat (limited to 'content')
-rw-r--r--content/numerik_1.tex6
1 files changed, 3 insertions, 3 deletions
diff --git a/content/numerik_1.tex b/content/numerik_1.tex
index 9934b22..eb607ab 100644
--- a/content/numerik_1.tex
+++ b/content/numerik_1.tex
@@ -559,9 +559,9 @@ $$\|y''\|_2 := \left(\int_a^b y''(t)^2 dt\right)^{1/2}$$
Für $s \in S_{4,\Delta}$, $\Delta = \{t_0,\cdots,t_{l+1}\}$ sind mögliche Randbedingungen:
\begin{enumerate}[label=(\alph*)]
- \item $s'(a) = f'(a)$ und $s'(b)=f'(b)$, \emph{vollständige Spline-Interpolation}
- \item $s''(a) = s''(b) = 0$, \emph{natürliche Interpolation}
- \item $s'(a) = s'(b)$ und $s''(a) = s''(b)$ falls $f$ periodisch mit Periode $b-a$, \emph{periodische Interpolation}
+ \item $s'(a) = f'(a)$ und $s'(b)=f'(b)$: \emph{vollständige Spline-Interpolation}
+ \item $s''(a) = s''(b) = 0$: \emph{natürliche Interpolation}
+ \item $s'(a) = s'(b)$ und $s''(a) = s''(b)$ falls $f$ $b-a$ periodisch: \emph{periodische Interpolation}
\end{enumerate}
Ist eine dieser Randbedingungen erfüllt, so ist $s$ eindeutig bestimmt. Ferner gilt für alle anderen interpolierenden $y \in \mathcal{C}^2(a,b)$: $\|s''\|_2 < \|y''\|_2$