Build polynomial and spline interpolation and expose the Runge phenomenon.
A spec, not a walkthrough. Build an interpolation module offering Lagrange, Newton divided-difference, and cubic-spline interpolation, then use it to demonstrate why high-degree polynomial interpolation on equally spaced nodes fails (Runge).
Implement lagrange(x, y), newton_divdiff(x, y), and use scipy CubicSpline. All three must reproduce the sample points exactly. Then interpolate Runge’s function 1/(1+25x²) and plot the error blow-up.
Acceptance criteria
0/4
Workspace
Deliverables
•A module with both hand-written interpolants + a spline demo.
•A plot comparing polynomial vs spline on Runge’s function.
Stretch goals
•Add Chebyshev nodes and show they cure the Runge blow-up.
•Report the max interpolation error vs polynomial degree.