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b/semester3/numcs/parts/01_interpolation/02_piece-wise/02_splines.tex index 87319c4..523e35f 100644 --- a/semester3/numcs/parts/01_interpolation/02_piece-wise/02_splines.tex +++ b/semester3/numcs/parts/01_interpolation/02_piece-wise/02_splines.tex @@ -81,9 +81,9 @@ Die Matrix ist nun also positive-definite und symmetrisch \inlineremark Die SLE können in $\tco{n}$ gelöst werden. -\inlineremark Mit der ``not-a-knot''-Bedingung $s'''$ ist stetig in $x_1$ und $x_{N - 1}$ braucht man mindestens $4$ Knoten. -Da wir kubische Splines betrachten erzwing die Bedingung dass ein Polynom nur in den ersten beiden und ein anderes in den letzten beiden Subintervallen erscheint, -also gilt $s_1 = s_2$ und $s_{N - 1} = s_N$ +\inlineremark Bei der ``not-a-knot''-Bedingung muss $s'''$ stetig in $x_1$ und $x_{N - 1}$ sein und man braucht mindestens $4$ Knoten. +Da wir kubische Splines betrachten erzwingt die Bedingung, dass ein Polynom nur in den ersten beiden und ein anderes in den letzten beiden Subintervallen erscheint, +also gilt $s_1 = s_2$ und $s_{N - 1} = s_N$. \inlineremark Der natürliche Spline minimiert die Gesamtkrümmung des Funktionsgraphen: \begin{align*}