Problem 19.16 presents the basics for a method to compute the eigenvalues of a positive definite matrix.  Implement a function choleig that takes a positive definite matrix  and executes maxiter...

Problem 19.16 presents the basics for a method to compute the eigenvalues of a positive definite matrix.

 Implement a function choleig that takes a positive definite matrix
 and executes maxiter iterations. After each iteration, use the MATLAB function spy to show the location of the nonzero entries as follows:

This will allow you to “watch” convergence to a diagonal matrix of eigenvalues. The function should verify that
is positive definite.

 Test choleig with the matrix

 Create a
 positive definite matrix using the code provided, and then run choleig with maxiter
 and watch convergence. Depending on the matrix, it may or may not graphically show as a diagonal matrix. In any case, check the results against eig (A).