灰色系统理论及其应用 (九) ： GM(1, N) 和GM(0, N) 模型
1 GM(1, N)https://img-blog.csdnimg.cn/20190430203704210.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI5ODMxMTYz,size_16,color_FFFFFF,t_70
https://img-blog.csdnimg.cn/20190430203725527.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI5ODMxMTYz,size_16,color_FFFFFF,t_70
https://img-blog.csdnimg.cn/20190430203741645.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI5ODMxMTYz,size_16,color_FFFFFF,t_70
https://img-blog.csdnimg.cn/20190430203815143.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI5ODMxMTYz,size_16,color_FFFFFF,t_70
2 GM(0, N) 模型
https://img-blog.csdnimg.cn/20190430203918275.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI5ODMxMTYz,size_16,color_FFFFFF,t_70
https://img-blog.csdnimg.cn/20190430203936598.png
GM(0, N) 模型不含导数，因此为静态模型。它形如多元线性回归模型但与一般的 多元线性回归模型有着本质的区别。一般的多元线性回归建模以原始数据序列为基础， GM(0, N) 的建模基础则是原始数据的1－AGO序列。
https://img-blog.csdnimg.cn/2019043020404795.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI5ODMxMTYz,size_16,color_FFFFFF,t_70
https://img-blog.csdnimg.cn/20190430204119384.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI5ODMxMTYz,size_16,color_FFFFFF,t_70
https://img-blog.csdnimg.cn/20190430204151942.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI5ODMxMTYz,size_16,color_FFFFFF,t_70
https://img-blog.csdnimg.cn/20190430204219749.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI5ODMxMTYz,size_16,color_FFFFFF,t_70
https://img-blog.csdnimg.cn/20190430204241695.png
计算的MATLAB程序如下：
clc,clear
x10=;
x20=;
n=length(x10);
x11=cumsum(x10)
x21=cumsum(x20)
for i=2:n
z11(i)=0.5*(x11(i)+x11(i-1));
end
B=[-z11(2:n)',x21(2:n)'];
Y=x10(2:n)';
u=B\Y
x=dsolve('Dx+a*x=b*x2','x(0)=x0');
x=subs(x,{'a','b','x0','x2'},{u(1),u(2),x10(1),'x21'});
digits(6),x=vpa(x);x=simple(x)
x=subs(x,{'t','x21'},{,x21(1:n)})
xhat=
epsilon=x10-xhat
delta=abs(epsilon./x10)
https://img-blog.csdnimg.cn/20190430204337201.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI5ODMxMTYz,size_16,color_FFFFFF,t_70
https://img-blog.csdnimg.cn/20190430204404528.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI5ODMxMTYz,size_16,color_FFFFFF,t_70
计算的MATLAB程序如下：
clc,clear
x10=;
x20=;
n=length(x10);
x11=cumsum(x10)
x21=cumsum(x20)
B=;
Y=x11(1:n)';
u=B\Y
x11hat=B*u
x10hat=
epsilon=x10-x10hat
delta=abs(epsilon./x10)
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原文链接：https://blog.csdn.net/qq_29831163/article/details/89715415
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