Minimax Equioscillation Error

Compare uniform, squared-error, and interpolation objectives through equioscillating residuals.

Experiment

Open the Minimax Equioscillation Error module and follow these steps to see the differences between approximation methods.

1. Set the Target to "Cubic".
2. Set the Approximation to "Minimax". Observe the uniform error on the interval, which should be 0.25. The residual curve oscillates evenly between -0.25 and 0.25, hitting the extrema 4 times.
3. Change the Approximation to "Least squares". The error curve no longer equioscillates, and the uniform error on the interval increases, but the overall squared area under the residual curve is minimized.
4. Change the Approximation to "Node interpolation". The residual curve passes exactly through the endpoints (and other specific nodes depending on the target), but can result in much larger maximum errors between nodes.
5. Change the Probe x value to see the exact numeric values of the approximation, target, and signed residual at different points.