Practice question · True or false
A high-degree polynomial forced through many equally spaced points approximates the underlying function better than a low-degree one.
Hints
- What happens near the ends of the interval?
- Runge's phenomenon.
Show the answer
False
Why
False. Raising the degree makes the interpolant oscillate violently near the ends of the interval, Runge's phenomenon, so it matches at the nodes and is badly wrong between them. Splines avoid it by staying low-degree and piecewise, and Chebyshev nodes avoid it by clustering points toward the ends.
Practise Interpolation and Curve Fitting
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