(a) Implement the subspace iteration in MATLAB. To test your code, run MATLAB command load west0479;

(a) Implement the subspace iteration in MATLAB. To test your
code, run MATLAB command load west0479; and compute the 8 eigenvalues of
largest modulus to relative tolerance 10−8 . Compare your computed
eigenvalues with those obtained from MATLAB command eigs(west0479,8,`lm'). You
may use the command [X,˜] = qr(X,0) to orthonormalize Xk+1 . (b) Implement the
shift-invert subspace iteration. Make sure to use lu to factorize A −
σI before the for loop and use the LU factors to solve the linear systems
(A − σI)Xk+1 = Xk . To test your code, compute the 6 eigenvalues
around σ = 1 of west0479 to relative tolerance 10−8 . Compare your
results with those obtained from command eigs(west0479,6,1).