Interpolation is a modeling choice.
All three methods pass through the data. What changes is what they assume between observations: one global polynomial, independent local lines, or smooth local cubics joined together.
Interpolation · CMNA Laboratory
One set of points. Three very different curves.
Paste data into R, then compare a global polynomial, local line segments, and a natural cubic spline across exactly the same samples.
Bring your own data
Define x and y in R.
The lab builds all three interpolants in R and lets you sweep across x to compare their values.
Runtime
Preparing R…RDefine numeric vectors
x and yPolynomialPiecewise linearCubic spline
| point | x | y |
|---|
Book§4.1–4.2 · Polynomial and Piecewise Interpolation · pp. 89–103Book details
TeachingInstructor notes and chapter contextOpen teaching material
Numerical ZooWorked problems