CAS Experiment
(a) Write a program for the iteration in Example 4 (with any A and x0) that at each step prints the mid point (why?) the endpoints, and the length of the inclusion interval.
(b) Apply the program to symmetric matrices of your choice. Explore how convergence depends on the choice of initial vectors. Can you construct cases in which the lengths of the inclusion intervals are not monotone decreasing? Can you explain the reason? Can you experiment on the effect of rounding?