Fido 22:31 87%- A. Computing Assignment Polynomial interpolation and node distribution Required submission: 1 page PDF document and scripts/codes uploaded to Canvas The purpose of this assignment is to examine how the locations of the nodes zo.z! zn afect the accuracy and robustness of polynomial interpolation. To compute the interpolating polynomial you will be using the barycentric form described in lectures. For this, you need to download the matlab functions baryweights.m and barginterp m from the computing assignment page in Canvas. The first computes the weights ub-t b- of the barycentric form and the second computes the To begin, consider the equally-spaced nodes on -1, 1. siven by 2i Write code to compute the error of the interpolating polynomial for some suitable range of n (in practice, you should replace this maximum by the maximm on some suficiently fine grid) and plot log10(%) versus n for the test functitE Using this, comment on the accuracy of polynomial interpolation at equally-spaced nodes. Next, consider the so-called Chebyshee nodes on -1, 1], given by Repeat the previous experiment with these nodes instead of (1) and test it on the functions above. Note that in this case you should not use the function baryweights m to find the weights, but instead use the known formula if you don't do this, your computation may result in under/overflow). Is polynomial interpolation at Chebyshev nodes accurate? Is it robust? Finally, use the Chebyshev nodes to approximate the function fs(z) = cos(10%). Find the smallest value of n (to within 10) such that en 10-5