Page 118 - Algorithm Collections for Digital Signal Processing Applications using MATLAB
P. 118
106 Chapter 3
Represent the matrix U o as the linear combinations of Eigen vectors.
2
1 =
0
-0.8503 -0.1412 - 0.3752i -0.1412 + 0.3752i c1
-0.4623 -0.3094 + 0.4471i -0.3094 - 0.4471i c2
-0.2514 0.7374 0.7374 c3
c1 -2.0649 + 0.0000i
c2 = -0.3520 + 0.1929i
c3 -0.3520 - 0.1929i
U 1 = A U o
2
U 2 = A U o
…
k
U k = A U o
U o = c1*E1+c2*E2+c3*E3
AU o = c1*A*E1+c2*A*E2+c3*A*E3
= c1*λ 1*E1+c2*λ 2*E2+c3*λ 3*E3
Similarly
k
k
k
k
U k = A U o = c1*λ 1 *E1+c2*λ 2 *E2+c3*λ 3 *E3
Therefore U 100 is computed as
U 100 = 1.0e+026
5.1220 - 0.0000i
2.7848 - 0.0000i
1.5140 - 0.0000i
Therefore the 100th term in the sequence is given as 1.51401.0e+026
th
Let us compute 6 term using the method given above
