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Polynomial Interpolation: Extrapolation

Extrapolation

Extrapolation is the process of predicting a value that lies outside the range of the known base points. Extrapolation using polynomials should be treated with extreme care. For example, the Runge function described above predicts, when x=1.2, the value of y=\frac{1}{1+25(1.2)^2}=0.027. Had we used extrapolation using the fitted polynomial, the predicted value would have been y=-146.372 which does not really follow the trend of the interpolated points!

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