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(ti,xI)=i=1,n
X=at+b(1)
b- .
Y(a,b)=sum(ati+b)-xi)2(2)- ,
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dy(a,b)/da=0
dy(a,b)/db=0
a b, .
dy(a,b)/da=d/da[sum(ati+b)-x1)2]==sum(ati-xi)+bn=0 (3)
dy(a,b)/db=d/db[sum(ati+b)-x1)2]==a sum ti2+b sum ti-sum tixi=0 (4)
3 4 .
a sum ti2+b sum ti-sum tixi (5)
a sum ti+bn= sum xi (5)
2 , .
.
ti | xi | tixi | ti2 |
Sum ti=28, sum xi=56, sum tixi=223, ti2=140
5 .
140a+28b=223 (6)
28a+7b=56 (6)
6,
a=-0.04 (7)
b=8.14 (8)
1 7
x=-0.04t+8,14 (8)
8 .
f8=-0.04*8+8,14=7,82
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maxmin ai,j=/ minimax ai,j .
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minmax aij - maxmin aij=3-2=1>0 (3)
maxmin aij, minmax aij
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X=(0,2;0,4;0,1;0,3)
X=(0,1;0;0)
Y=(y1,y2yn)
y1=>0;y2=>0;yn=>0
sum yj=1
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H(X,Y)=XAYT (2)
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X*AY*T<X*AY*T<=X*AYT (3)
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, maxmin XAYT minmax XAYT.