灰色模型 - 数学建模社区-数学中国

clear
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syms a b;
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c=[a b]';& K; A5 f: Q7 O! z# ^% q
A=[539.658590944408,544.467335019023,543.118901615168,541.395536784412,539.719603563031,538.320685053971,536.799895148485,539.869612431029,534.915223499512,544.533125668254];3 c1 R# T3 |& p2 o& E
B=cumsum(A);# @+ _- i- I$ E
n=length(A);. c9 Z7 D+ y2 k2 `( q4 \6 u
for m=1:(n-1)
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C(m)=(B(m)+B(m+1))/2;0 j( @9 k5 s2 G. M6 c- m
end0 f& R: v- y8 k5 [6 W
D=A;; v; e. g+ ?# {) f6 i4 J4 o
D(1)=[];
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D=D';4 x5 f i* D0 t6 [2 e( K
E=[-C;ones(1,n-1)];
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c=inv(E*E')*E*D;( D/ V! Z& v* q; y/ E
c=c';0 a1 h/ i( A$ n+ K& E3 A
a=c(1);
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b=c(2);& u. \% x. ^/ N) d
F=[];
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F(1)=A(1);& g( P0 o- |# i; X e
for m=2:(n+10)
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F(m)=(A(1)-b/a)/exp(a*(m-1))+b/a;
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end
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G=[]; V: r* x+ ?9 e: u8 ~
G(1)=A(1);
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for m=2:(n+2)0 Z6 g% N8 K# d) f) ` d6 P
G(m)=F(m)-F(m-1);
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end
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t1=1:10;
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t2=1:12;; C/ ]7 e' W* n c7 T
plot(t1,A,'r',t2,G,'g')
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