A New Optimization Approach for Grey Model GM(1,1) - Advanced Research on Computer Education, Simulation and Modeling - page 121

Table 1. Data of Financial Input in Science and Technology of 1997~2003 Years

<HDU

'DWD

+XQGUHG PLOOLRQ <XDQ

Based on the data of 1997~2002 years, we establish GM (1, 1) model by the
method in this paper and obtain the recuperating formula as follows:

(0) 0.1727 k

xk ˆ ( += ) . 4 e k = 1, 2, L

Finally we obtain the following results:

Table 2. Comparision of the Simulation Precision

/LWHUDWXUH>@ 0HWKRGRIWKLVSDSHU

$FWXDO
YDOXH

<HDU

6LPXODWHG
YDOXH

5HODWLYH
HUURU

5HODWLYHHUURU 6LPXODWHGYDOXH

Table 3. Comparision of the Prediction Precision

Literature [4] Method of this paper

Actual
value

Year

Relative
error(%)

Predicted value Relative error(%) Predicted value

2003 21.22 21.616 1.8662 21.2826 0.2827

From table 2 and table 3, we find that the method of this paper has higher simulation
precision and prediction precision than Literature [4].

3 Conclusions

In this paper first of all, we choose (1.2) as the background value of the new model,
then obtain development coefficient a , and we have proved that it has no deviation
between development coefficient a and the actual coefficient a for the normal
exponential series under the new background value
After the development coefficient a was fixed, the parameter c in the
recuperating values

xk −

(0) ak ˆ

L is determined by (1.3). This
method can guarantee that it also has no deviation between coefficient c and the
actual coefficient c for the normal exponential series.

ˆ () = ˆ

( k = , , , n )