Practice question · Multiple choice
Fitting a polynomial through all n data points guarantees passing through every one, and Runge showed the result can oscillate wildly between them. What is the fix in practice?
Hints
- A high-degree polynomial is one object over the whole interval. Ask what that means for locality.
- Runge's phenomenon is worst with equally spaced points. Does spacing alone solve it?
Show the answer
B. Splines, low-degree pieces joined smoothly to keep it local
Why
A single high-degree polynomial is global, so every coefficient answers to every point and the curve whips about near the ends. Splines make it local, cubic pieces meeting smoothly, which is why they are what CAD, fonts and animation actually use.
Practise Interpolation and Curve Fitting
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