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Cubic Splines MACM 316 15/15<br />
Second Example<br />
Consider the following data representing the thrust of a model<br />
rocket versus time.<br />
t T<br />
0.00 0.00<br />
0.05 1.00<br />
0.10 5.00<br />
0.15 15.00<br />
0.20 33.50<br />
0.30 33.00<br />
0.40 16.50<br />
0.50 16.00<br />
Below is a plot of the natural spline:<br />
Thrust<br />
40<br />
35<br />
30<br />
25<br />
20<br />
15<br />
10<br />
5<br />
t T<br />
0.60 16.00<br />
0.70 16.00<br />
0.80 16.00<br />
0.85 16.00<br />
0.90 6.00<br />
0.95 2.00<br />
1.00 0.00<br />
0<br />
0 0.2 0.4 0.6 0.8 1<br />
time<br />
Notice how wiggles are introduced near the ends of the flat region<br />
– non-smooth data cause some problems for cubic <strong>splines</strong>.<br />
November 1, 2012 c○ Steven Rauch and John Stockie
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