AACAS Newton Form of The Interpolating Polynomial Question

AACAS Newton Form of The Interpolating Polynomial Question

Newton Form of The Interpolating Polynomial Question

 

(27 points) Given the points (Xi, Yi) for i = 0…n the Newton form of the interpolating polynomial is p(x) = do + a1(x – Xo) + + An (x – xo)(x – x1)… (x – Xn-1). The textbook provides code for computing the coeffients by a divided difference table and evaluating the polynomial. I provided this code on the class website. = (a) Compute the coefficients of the Newton form of the interpolating polynomial for the fifth degree polynomial that interpolates f(x) cos(21x) at the points x; j/5 for j = 0,…,5. Display the results in a table. (b) Make a plot of f(x) and the interpolating polynomial, p(x), from part (a) on the same axes for 0 < x < 1. Plot the difference of f and p for 0 < x < 1. (c) Estimate the maximum of f(x) – p(x)| on the interval [0, 1] by evaluating f and p for a large number of points between 0 and 1. (d) Evaluate p(1.5), p(2.0), and p(2.5) and report the results. Why are the values of p so different from the values of f at these points compared to points in [0, 1]?
Purchase answer to see full attachment