Numerical Methods Course Notes Version 0.1 (UCSD Math 174, Fall ...
Numerical Methods Course Notes Version 0.1 (UCSD Math 174, Fall ...
Numerical Methods Course Notes Version 0.1 (UCSD Math 174, Fall ...
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68 CHAPTER 5. INTERPOLATION<br />
1<br />
0.8<br />
runge<br />
3 nodes<br />
7 nodes<br />
10 nodes<br />
0.6<br />
0.4<br />
0.2<br />
0<br />
-0.2<br />
-0.4<br />
-6 -4 -2 0 2 4 6<br />
(a) 3,7,10 equally spaced nodes<br />
8<br />
7<br />
runge<br />
15 nodes<br />
100000<br />
0<br />
runge<br />
50 nodes<br />
6<br />
-100000<br />
5<br />
-200000<br />
4<br />
-300000<br />
3<br />
2<br />
-400000<br />
1<br />
-500000<br />
0<br />
-600000<br />
-1<br />
-6 -4 -2 0 2 4 6<br />
-700000<br />
-6 -4 -2 0 2 4 6<br />
(b) 15 equally spaced nodes<br />
(c) 50 equally spaced nodes<br />
Figure 5.3: The Runge function is poorly interpolated at n equally spaced nodes, as n gets large.<br />
At first, the interpolations appear to improve with larger n, as in (a). In (b) it becomes apparent<br />
that the interpolant is good in center of the interval, but bad at the edges. As shown in (c), this<br />
gets worse as n gets larger.