Exercise 3 Let(z))0,..,N be the set of Lagrange characteristic polynomials associated with the nodes [xj)j-o..,.v. We have seen in class that the polynomial interpolation error is related to the Lebesgue function N(x)(Lebesgue function), 0 and the Lebesgue constant Amax AN() (Lebesgue constant) 1. Given the vector of interpolation nodes x=[xi(1) . . . xi (N+1), write a Matlab/Octave Use the Matlab command x-linspace(-1,1,1000) to generate a vector of 1000 evenly spaced nodes in [-1, 1] function compute Lebesgue function.m that returns the Lebesgue function (4) and the Lebesgue constant (5). Such function should be of the form function [lambda,L]-compute Lebesgue-function(xi,x) Input n: vector of interpolation nodes xi= [xi (1) . . . x (N+1)] x: vector of points at which we want to evaluate the Lebesgue function Output lambda: Lebesgue function AN(x) evaluated at x L: Lebesgue constant AN, computed by taking the maximum of the vector 1ambda