-
next we arrange the largest element in AV0 to
be 1. Let this be done by dividing the vector
V0 by b0 to get vector
V1 = (1/b0)(k1t1v1 +
k2t2v2 +
k3t3v3 +
k4t4v4)
which can be written as
V1 =
(t1/b0)(k1v1 +
k2(t2/t1)v2
+
k3(t3/t1)v3
+
k4(t4/t1)v4
-
the next estimate V2 is obtained by multiplying
V1 and arranging the largest element to be 1, we
get
V2 =
((t1)2/b0b1)(k1v1 +
k2(t2/t1)2v2
+
k3(t3/t1)2v3
+
k4(t4/t1)2v4
-
continuing with the process for m iterations we get the
mth estimate of the vector
Vm =
((t1)m/b0b1...bm-1)(k1v1 +
k2(t2/t1)mv2
+
k3(t3/t1)mv3
+
k4(t4/t1)mv4
-
since t1 is numerically greatest of all the Eigen
values, as m increases
(t2/t1)m,
(t3/t1)m, ... will tend to
zero.Vm = ((t1)m/b0b1...bm-1)(k1v1)
-
multiplying by A we get
AVm =
((t1)m/b0b1...bm-1)(k1Av1)
          = t1
((t1)m/b0b1...bm-1)(k1v1)
AVm = t1Vm
-
hence the mth estimate of the Eigen vector gives the maximum Eigen value and the
corresponding Eigen vector