Least Squares Polynomial Fits Write the MATLAB function x = clsq(A, b, B, d) that solves the equality constrained least squares problem min_x{||Ax-b||_2: Bx = d} for the ease that A is 1-1 and B is onto. Use the QR factorization on B as described in class, and call lsq() to handle the unconstrained sub-problem. Find the best Least Squares polynomials p(x) = Sigma^n _i = 0 alpha_i x^i degrees n = 1, 2, 3 and 4 that fits the data {(0.0042, 0.9924), (0.2025, 0.9434), (0.1080.0.4941), (0.5968, 0.4535), (0.7999, 0.1985), (0.9970, 0.2272)}. Also find the polynomial interpolant (of appropriate degree) and the quadratic least squares fit with constraints p(x_1) = y_1, p(x_6) = y_6 and p'(x_6) = D where D the first divided difference between (x_5, y_5) and (x_6, y_6). Once von get your coefficients alpha, you can use polygala () to evaluate the polynomial and plot. Least Squares Polynomial Fits Write the MATLAB function x = clsq(A, b, B, d) that solves the equality constrained least squares problem min_x{||Ax-b||_2: Bx = d} for the ease that A is 1-1 and B is onto. Use the QR factorization on B as described in class, and call lsq() to handle the unconstrained sub-problem. Find the best Least Squares polynomials p(x) = Sigma^n _i = 0 alpha_i x^i degrees n = 1, 2, 3 and 4 that fits the data {(0.0042, 0.9924), (0.2025, 0.9434), (0.1080.0.4941), (0.5968, 0.4535), (0.7999, 0.1985), (0.9970, 0.2272)}. Also find the polynomial interpolant (of appropriate degree) and the quadratic least squares fit with constraints p(x_1) = y_1, p(x_6) = y_6 and p'(x_6) = D where D the first divided difference between (x_5, y_5) and (x_6, y_6). Once von get your coefficients alpha, you can use polygala () to evaluate the polynomial and plot