Carry out the numerical experiment described in and construct a plot like that in Recall that the function i, not builds the biharmonic matrix discussed in Section The reader should consult the...

Carry out the numerical experiment described in

and construct a plot like that in

Recall that the function i, not

builds the biharmonic matrix discussed in Section

The reader should consult the MATLAB documentation to determine the action of sprandn. Generate a

random sparse matrix using the MATLAB statements

The eigenvalues of

are complex. Apply the Arnoldi process to generate a matrix

₃₅

and compute its eigenvalues, the Ritz values. Then compute the eigenvalues of

using eig and plot them marked with a circle, followed by a plot on the same axes of the Ritz values marked by

displays the results. Note that the largest and smallest Ritz values in magnitude are close to eigenvalues of

This is typical behavior.