Practice question · Select all that apply
Twenty-one exact data points are to be interpolated. Select every genuine reason to prefer a cubic spline to a single degree-20 polynomial.
Hints
- A spline is still an interpolant, check what that rules out.
- Both options use all 21 points; the difference is in the degree of the pieces.
Show the answer
- A. High-degree interpolating polynomials can oscillate wildly between the data points.
- B. Least squares minimises the sum of squared residuals.
- C. A spline joins low-degree pieces smoothly rather than using one high-degree polynomial.
Why
The spline interpolates, so it hits every point while keeping each piece cubic and locally tame. It is not a least-squares fit and it uses exactly the same data, those two options describe a different method altogether.
Practise Interpolation and Curve Fitting
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