Question
Numerical Methods. Part b involves the use of Matlab. Please show all work.
Consider the problem of computing a Newton polynomial to interpolate values of the function f(x) = x3 - 4x, based o n nodes between x = 1 and x = 6. Compute values of the error function based on the following settings. Note that c is a number somewhere in the interval [1, 6]. In each case compute an upper bound on the error value by finding the maximum value of the (N + l) th derivative over the interval. N = 1 with x0 = l and x1 = 6 N = 2 with x0 = l, x1 = 3.5 and x2 = 6. N = 5 with x0 = 1, x1 = 2, x2 = 3, x3 = 4, x4 = 5 and x5 = 6. Plot the interpolation polynomials you find for i., ii and iii above and confirm that the error you found agrees with the estimate you made in part a).
Explanation / Answer
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