Question

Problem 1. (20) The purpose of this exercise is for you to get familiar with MATLAB and some of its capabilities. We have seen in class that, for a positive integer n and data {(rj, yj)|j= 0,...n}, the matrix system produces the coefficients of the polynomial Pn(x) coc1x++ cn&" that interpolates the data, where [Vn]ij = x;_{ for 1 < i,j <n+1. Let r j/n, giving a uniformly spaced set of n 1 points in [0, 1]. Write a MATLAB program that plots approximations to the functions f (x) = r* for r = 0,1,... , n on the interval 0, 1 for n = 1, 7, and 15, using these evenly spaced points for input For each n, the program should produce a single figure containing xy-plots of {(xj, xf) |j= 0,... , n} for each r0,.,n place the title "n=(value-of-n)" at the top of this figure plot x- and y-axes, in black plot the data so that it is easy to read, by allowing some space to be visible around the ends of the axes, and SO format the figure in a square display The program should also run in an aesthetically pleasing way. For example, when it is producing the plots, you should have the program pause for a small amount of time (say, 1/2 second) so that you can see the results appear, and you should also have it pause between different values of n The results turned in should be your program, properly commented, two (of the three) figures produced, and the tabulated set of condition numbers