Question: 5 (a) Use Newton basis functions for determining the polynomial interpolant for the data points (1, 0), (2, 12), (3,38). Construct the basis matrix and

5 (a) Use Newton basis functions for determining the polynomial interpolant

5 (a) Use Newton basis functions for determining the polynomial interpolant for the data points (1, 0), (2, 12), (3,38). Construct the basis matrix and solve for the coefficients using forward substitution. (b) Now use the divided differences scheme to compute the coefficients. Show the steps in your (c) Given an additional point (4,84), incrementally construct the cubic polynomial that interpo- (15 points) calculations. lates all four points

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