Information Technology Reference
In-Depth Information
⎛
(0)
⎞
(1)
x
x
(2)
(3)
⎛
−
z
z
(2)
1
⎞
⎜
⎟
⎜
⎟
,
. Then
(0)
−
(1)
(3)
1
⎜
⎟
⎜
⎟
Y
=
⎜
B
=
⎜
⎟
⎟
M
M
M
⎜
⎟
⎜
⎟
⎜
⎟
⎜
⎟
(0)
(1)
x
()
n
−
z
() 1
n
⎝
⎠
⎝
⎠
A.
According to the least square method, we have
, and
(
)
−
1
(
)
T
ˆ
T
T
α
=
ab
,
=
B B
B Y
n
n
n
∑∑ ∑
(1)
( 0)
(1)
( 0)
zk xk n
()
() (
−−
1)
zkxk
()
()
a
ˆ
=
k
=
2
k
=
2
k
=
2
(1.1)
2
n
⎛
n
⎞
∑
∑
( )
n
−
z
(1)
()
k
2
−
z
(1)
()
k
⎜
⎟
⎝
⎠
k
=
2
k
=
2
(1)
dx
B.
The time response of white differential equation
is
+
ax
(1)
=
b
dt
b
b
⎛
⎞
(1)
(1)
−−
at
(
1)
xt
()
=
x
(1)
−
e
+
⎜
⎟
a
a
⎝
⎠
(0)
(1)
xk zk b
()
+
()
=
C.
The time response of grey differential equation
is
b
b
⎛
⎞
(1)
(1)
−−
ak
(
1)
xk
()
=
x
(1)
−
e
+
⎜
⎟
a
a
⎝
⎠
D.
The recuperating value is
⎛
b
⎞
(0)
(1)
(1)
a
(0)
−
ak
xk
ˆ
( )
+=
xk
ˆ
( )
+−
xk
ˆ
() 1 ) )
=−
e x
−
e
,
k
=
1, 2 , 3,
L
.
⎜
⎟
a
⎝
⎠
b
⎛
b
⎞
(1)
−
ak
Let
⎠
,
,then
xk
(
+=
)
ce
+
c
is the non-homogeneous
c
=
x
(1)
(1)
−
c
=
⎜
⎟
1
2
1
2
a
a
⎝
b
⎛
⎞
exponential form. Let
c
=−
(1
e
a
)
x
(0)
(1)
−
⎠
, then
ˆ
xk
(0)
(
+=
)
−
ak
is the
⎜
⎟
a
⎝
homogeneous exponential form. Therefore, if only working out
a
and
c
we could
obtain the recuperating values. For
the parameter
a
, we utilize (1.1) to obtain
a
. Here
it is also very important for selection of background value. This paper takes the new
background value derived in literature [4], its derivation
principle is based on the fact
that
(1)
xk
−−
(0)
=
ak
(
1)
x
has the non-homogeneous exponential form, where
()
(
k
=
, ,
L
, i.e.,
)
a
k
k
g
ge
∑∑
xk
(1)
()
=
x i
( 0 )
()
=
−−
ai
(
1)
=
e
−−
ak
( )
+
=
ge
−−
ak
( )
+
g
1
2
1
−
e
a
e
a
−
1
i
=
1
i
=
1
Brief process as follows:
Search WWH ::
Custom Search