Interpolation

When to Use

Use this skill when working on interpolation problems in numerical methods.

Decision Tree

1. Assess Data Characteristics

   • How many data points? Spacing uniform or non-uniform?
   • Is data smooth or noisy?
   • Need derivatives at endpoints?

2. Select Interpolation Method

   • Few points (<10): Polynomial (Lagrange, Newton)
   • Many points, smooth data: Cubic splines
   • Noisy data: Smoothing splines or least squares
   • High dimensions: Use simplex-based (n+1 neighbors vs 2^n)