Let A Rnxn be a real symmetric matrix. We denote the eigenvalues by 11, ..., In ER and assume that \1 is dominant and non-zero, that is, 1111 > Mil for all i = 2, ..., n. Consider the following Matlab program: = 1 A % (input) 2 TOL % Termination tolerance (input) 3 [v_min, d_min] = eigs (A,1, 'smallestabs'); 4 [v_max, d_max] eigs (A,1, 'largestabs'); 5 v = v_min; 6 while norm (v-v_max) >TOL && norm (v+v_max) >TOL A*vorm (A*v); 8 end V = a) Provide a brief explanation of why the program should not terminate in theory, but why it does in practice. b) Provide for the matrix A = [1,2; 2,3] a modification of the program such that the dominant eigenvalue of A is approximated with a quadratic convergence rate. Explain in one to two short sentences your modification. Let A Rnxn be a real symmetric matrix. We denote the eigenvalues by 11, ..., In ER and assume that \1 is dominant and non-zero, that is, 1111 > Mil for all i = 2, ..., n. Consider the following Matlab program: = 1 A % (input) 2 TOL % Termination tolerance (input) 3 [v_min, d_min] = eigs (A,1, 'smallestabs'); 4 [v_max, d_max] eigs (A,1, 'largestabs'); 5 v = v_min; 6 while norm (v-v_max) >TOL && norm (v+v_max) >TOL A*vorm (A*v); 8 end V = a) Provide a brief explanation of why the program should not terminate in theory, but why it does in practice. b) Provide for the matrix A = [1,2; 2,3] a modification of the program such that the dominant eigenvalue of A is approximated with a quadratic convergence rate. Explain in one to two short sentences your modification