Author: Anonymous

How many data points (n) are needed for a 4th-order Newton polynomial interpolation? If xi =1, 1.5, 2, 2.5, 3, 4, 4.5, 5, 5.5, 6 and the corresponding f(xi) values are given, which values of xi would you select to estimate f(3.2) using a 4th-order Newton polynomial interpolation? Specify the selected values as x1, x2, …, xn                                                   (3 points)   2. The corresponding values of f(x) are provided at the following points: x=0, 1, 2, 3, 3.5, 4, 4.5, 5, 5.5, 6 Assuming that only Simpson’s rules may be used for numerical integration, explain how you would approach the evaluation of the integral over the given interval (0 to 6). Clearly indicate which Simpson’s rule(s) you would apply to each section and justify your choice.                      (3 points)   Construct amplitude and Phase line spectra for the following function. ​             for k = 1, 3, 5, 7                        (4 points)

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