Polynomial Interpolation) (a) Write a MATLAB function M-file called pv polyinter p (x, y) that…

Polynomial Interpolation) (a) Write a MATLAB function M-file called pv polyinter p (x, y) that will input two vectors x and y of the same length (call this length ” n +1 ” for now) that correspond to the JC- and ^-coordinates of n +1 data points on which we wish to interpolate with a polynomial of degree at most n. The output will be a vector pv-[an art_, ~-a2 a{ a0] that contains the coefficients of the interpolating polynomial p(x) = a„xn + a,.,χ””1 + · · · + a,x + a0 . (b) Use this program to redo part.. (c) Use this program to redo part (c) of Exercise 2. (d) Use this program with input vectors x = [0 nil π 3π/2 2π 5/r/2 3/r 7/r/2 4/r ], and _y = [10 -1 0 1 0 -1 0 1]. Plot the resulting polynomial along with the data points. Include also the plot (in a different style/color) of a trig function that interpolates this data.

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