Investigate the extrapolation characteristics of neural networks and polynomials. Consider the problem described in E11.25, where a sine wave is fit over the range -2- £ p £ 2. Select 11 training points evenly spaced over this interval.
i. After fitting the 1-2-1 neural network over this range, plot the actual sine function and the neural network approximation over the range -4 £ p £ 4
ii. Fit a fifth-order polynomial (which has the same number of free parameters as the 1-2-1 network) to the sine wave over the range -2 £ p £ 2 (using your results from E13.1 i.). Plot the actual function and the polynomial approximation over the range -4 £ p £ 4.
iii. Discuss the extrapolation characteristics of the neural network and the polynomial.