MATH 472 COMPUTING PROJECT # 4
Consider the matrix
A =
2
4
149 50 154
537 180 546
27 9 25
3
5
Part I Apply the stabilized power method to approximate the dominant eigenvalue
and corresponding eigenvector of A.
(1) Start the iteration with x
(0) = (1; 1; 1)T
.
(2) Stop the iteration when j?k ?k1j ? 105 where ?k is the Rayleigh quotient
?k =
x
(k)
T
Ax
(k)
x(k)
T
x(k)
(3) Print the number of iterations k, the Rayleigh quotient ?k and the corresponding eigenvector x
(k) at the end of the iteration.
Part II In this part, we use the Rayleigh Quotient iteration (see your class notes).
Use the same starting vector and the stopping criterion of Part I. Which method is
f
