mate our points. Then we'll duplicate our interpolating points and recalculate the approximating polynomial. The error for these points will go down. We'll keep duplicating them until the approximating polynomial fits them within the tolerable interpolation error.
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This works because what the approximation does, it minimizes the sum of squared residuals. If you put a point twice, its residual will be twice as important to the optimizer as any other point. If you add it 128 times, it will attract t