......................................... ..................

The results of the first two iterations presented above and subsequent iterations are presented in Table 2.1. These results were obtained on a 13-digit precision computer. The iterations were continued until A changed by less than 0.000001 between iterations. The final solution for the largest eigenvalue, denoted as AI' and the corresponding eigenvector XI is

AJ = 13.870584 and xi = [-0.291794] -0.143499 1.000000] (2.43) This problem converged very slowly (30 iterations), which is a large number of iterations for a 3 x 3 matrix. A procedure for accelerating the convergence of a slowly converging eigenproblem is presented in Example 2.5.