Write a MATLAB code of shift-invert subspace iteration, and compute the 3 eigenvalues of smallest modulus of this matrix, to tolerance 10^-12. Also plot the semilogy figure of the eigenresidual norm and report the number of iterations.

Hint: you might find the following statements useful:

Before we start the for loop, need

[L,U,P,Q,R] = lu(A-sigma*speye(size(A)));

Then in each iteration, we need

SX = Q*(U\(L\(P*(R\X))));

[X,~,~] = qr(SX,0);

(Could you please show the code and output so I can compare my answers. Thanks)