Matlab

The Hilbert matrix H_n of order n is defined with elements [H_n]_ij = 1/i + j - 1. In MATLAB, hilb (n) will generate H_n; use help hilb for more information. a. Compute the condition numbers of H_n in the infinity-norm for n = 2, ..., n_max, where n_max is the maximum value of n such that the condition number is less than 10^16. Save these condition numbers as an (n_max - 1) times 1 column vector in A1.dat using the "save -ascii" command. b. Let z_n be a n times 1 column vector whose entries arc all ones. Mathematically, z_n = H_n^-1 (H_n z_n) = H_n (H^-1 _n z_n). Computationally, there are numerical errors due to the large condition numbers. Compute the infinity-norm of ||z_n - H^-1 _n (H_n z_n)||_infinity and ||z_n - H_n (H^-1 _n z_n)||_infinity for n = 2, ..., n_max. Save these norms as (n_max - 1) times 2 matrix in A2.dat using the "save -ascii" command. The first and second columns correspond to the norms of ||z_n - H^-1 _n (H_n z_n)||_infinity and ||z_n - H_n (H^-1 _n z_n)||_infinity, respectively. The Hilbert matrix H_n of order n is defined with elements [H_n]_ij = 1/i + j - 1. In MATLAB, hilb (n) will generate H_n; use help hilb for more information. a. Compute the condition numbers of H_n in the infinity-norm for n = 2, ..., n_max, where n_max is the maximum value of n such that the condition number is less than 10^16. Save these condition numbers as an (n_max - 1) times 1 column vector in A1.dat using the "save -ascii" command. b. Let z_n be a n times 1 column vector whose entries arc all ones. Mathematically, z_n = H_n^-1 (H_n z_n) = H_n (H^-1 _n z_n). Computationally, there are numerical errors due to the large condition numbers. Compute the infinity-norm of ||z_n - H^-1 _n (H_n z_n)||_infinity and ||z_n - H_n (H^-1 _n z_n)||_infinity for n = 2, ..., n_max. Save these norms as (n_max - 1) times 2 matrix in A2.dat using the "save -ascii" command. The first and second columns correspond to the norms of ||z_n - H^-1 _n (H_n z_n)||_infinity and ||z_n - H_n (H^-1 _n z_n)||_infinity, respectively