Fitting Curves

Through the points, and the danger at the edges

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• n points determine exactly one polynomial of degree ≤ n − 1.
• With equally spaced points, high-degree interpolation can wiggle wildly (Runge’s phenomenon); Chebyshev points fix it.
• Splines join simple local pieces; exact fits extrapolate badly (overfitting).

Steps

1. Between two readings
2. One curve through all the points
3. Runge’s phenomenon
4. Splines
5. A parabola through three points
6. Beyond the data