Question Parts c,d,e,f,g

Consider the n n Wilkinson marr 1 001 1 10 Compute (by hand) the LU factorization of Ws . "Guess" the LU factorization of Wa, for any n. Write a MATLAB function w wilkin(n) that generates the n x n Wilkinson matrix. . Perform the following MATLAB experimen 4d.1 Generate A W6o- d.2 Let e e Roo be the column vector with all entries equal to 1. Form b-Ae 41.3 Use the backslash function to solve Ax = b. d.4 Compare the computed solution with the exact solution, x-e . Repeat the experiment in 4.d for smaller values of n. What is the largest value of n for which Wx-b can be solved accurately by GEPP f. Use the MATLAB functions cond (or condest) to compute or estimate the condition number of W for 10,20,.,60. Report your results in a table. Compare these results with the conditioning of the Hilbert matrix (hilb)). Based on this results, would you say that the Wilkinson matrix is ill-conditioned or well-conditioned? g. Cominent on the backward stability of GEPPS (= GE with Partial Pivoting and Scaling) on this problem. (Note that here PP no pivoting and that the matrix is already perfectly scaled Consider the n n Wilkinson marr 1 001 1 10 Compute (by hand) the LU factorization of Ws . "Guess" the LU factorization of Wa, for any n. Write a MATLAB function w wilkin(n) that generates the n x n Wilkinson matrix. . Perform the following MATLAB experimen 4d.1 Generate A W6o- d.2 Let e e Roo be the column vector with all entries equal to 1. Form b-Ae 41.3 Use the backslash function to solve Ax = b. d.4 Compare the computed solution with the exact solution, x-e . Repeat the experiment in 4.d for smaller values of n. What is the largest value of n for which Wx-b can be solved accurately by GEPP f. Use the MATLAB functions cond (or condest) to compute or estimate the condition number of W for 10,20,.,60. Report your results in a table. Compare these results with the conditioning of the Hilbert matrix (hilb)). Based on this results, would you say that the Wilkinson matrix is ill-conditioned or well-conditioned? g. Cominent on the backward stability of GEPPS (= GE with Partial Pivoting and Scaling) on this problem. (Note that here PP no pivoting and that the matrix is already perfectly scaled