3. (15 pts.) Recall that the Chebyshev interpolation nodes over the interval (-1, 1] are given by the formula r; s(") for j 1,2, .n. = COS (2j- (a) Find an upper bound for the error for x E -1, 1]...

Extracted text: 3. (15 pts.) Recall that the Chebyshev interpolation nodes over the interval (-1, 1] are given by the formula r; s(") for j 1,2, .n. = COS (2j- (a) Find an upper bound for the error for x E -1, 1] when the above Chebyshev nodes are used to approximate f(r) erp(-4r?) with n = 6. The bound for error with 6 steps was found to be 7.0806e +05 (b) Write a MATLAB code to interpolate f(x) [-1, 1] with n = 6. Make a plot showing the interpolation data, the exact function f(x), and the polynomial interpolant. Make a second plot showing the error between the interpolant and f(x). How does the maximum error shown in this plot compare to your estimate? exp(-4r2) at the Chebyshev nodes for x E (c) Write a MATLAB code to interpolate f(r) = erp(-4r) at the Chebyshev nodes for x e -1, 2] with n = 8. Make a plot showing the interpolation data, the exact function f(x), and the polynomial interpolant. Make a second plot showing the error between the interpolant and f(x).