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zBZ&Dxpc(@>lVcXrf-=2wbZRdk&$^ViT}NWxMyH?Onb{sq=aD~at=|~Va zflmsahCY?yXMjA5xav6o)-t85luq+!9cn`hCyLeN6`e3Q0%;IXPAIRDu5o Da=3X> diff --git a/semester3/numcs/parts/01_interpolation/00_polynomial/02_newton-basis.tex b/semester3/numcs/parts/01_interpolation/00_polynomial/02_newton-basis.tex index e870b84..b0689ea 100644 --- a/semester3/numcs/parts/01_interpolation/00_polynomial/02_newton-basis.tex +++ b/semester3/numcs/parts/01_interpolation/00_polynomial/02_newton-basis.tex @@ -87,6 +87,10 @@ Falls $x_j = x_0 + \underbrace{j \cdot h}_{:= \Delta^j}$ gilt vereinfacht sich e (D.h. die dividierten Differenzen sind korrekt.) \normalsize +\fancyex{Runge-Funktion} Die Runge-Funktion kann am Rand des gewählten Intervalls starke Oszillationen in der Interpolation verursachen, +wenn bspw. die Stützstellen nicht gut gewählt sind oder das Polynom einen zu hohen Grad hat. +Sie ist definiert durch $\displaystyle f(x) = \frac{1}{1 + x^2}$ + \newpage \begin{multicols}{2}