1. Repeat Worksheet 6 Q1 for the barycentric formula, i-0 i-0 where we have defined the "barycentric weights" j-0 While mathematically equivalent to the Lagrange interpolation formula, the barycentric formula has the prac- tical advantage that the bulk of the computation computing the barycentric weights can be performed "offline" and is efficiently updatable to include more interpolation points. (a) Implement this as a Matlab function with the signature function y -linterp_bary(X, Y, x) (X and Y are arrays containing ro, ...,Tn and yo,... , Jn, resp.) You may not use any of Matlab's polynomial routines (like polyfit or interp1) nor the Symbolic Math Toolbox. Test your code by 1. picking your favorite polynomial p of degree five 2. populating X with six distinct numbers, 3. setting Y to be p evaluated at the corresponding entries of X, using polyval, 4. picking x to be a number besides those in X, 5. comparing p(x) with linterp_bary (X, Y, x) For example, implement rHr5-1 by p-0(x) polyval([1 0 0 0 0-1], x); (b) Extend your code to allow x to be an array, so that y is an array of the same dimensions, each entry being the Lagrange interpolation formula evaluated at the corresponding entry of x. Reusing from Part (a) the polynomial function p and the arrays X and Y, run the following commands xlinspace (min(X)-1, max (X)+1, 100); plot(x, p(x), 'ko:', x, linterp_bary(X, Y, x), 'rx: '); The red xs should coincide with the black os