3 ""
"- () (-
) ".
" "
1. .
- -
. F(X1,X2), ( -
) , .
F(X1,X2,X3), (-
). ,
.. , ,
.
, ()
( F(X1,X2))
(), :11,X21; X12,X22;
X13,Y23. (.1)
F1(11,X21), F2(X12,X22), F3(X13,Y23) .
, -
, F(X1,X2) , -
( , ). , , F1<F2
F1<F3, , ,
2 3 , , 4.
. (.2)
4 F4(X14,X24). -
2,3,4.
- 2 -
X2 I 2 I
I I
I o 3 I o 3 o 4
I 1 o o 2 I 1 o o 2
I ______________ X1 I_________________ 1
.1 .2
,, F2<F4 F2<F3 5
2, 3 4. -
F 3,4 5 -
6 .. -
F.
, -
, .
F -
.
F - " " .
- ,
( ) -
D, , ,
,, : D=(D1*D2*D3..Dn)^1/n
Xi -
() Xi: Summa(Ki*(Xi-Xi)^2). i
() i.
, , K1=K2=...=Kn=1.
|
|
2. .
,
, .
2 3 F .
-
- 3 -
4 5. F 5 , -
,
F , .
.
.
, 100.
, F
.
,
.
, , .
. -
Simplexg. -
2(1).
,
.
- .
-
-
.
3. .
-
,
.
-.
4
" ".
" "
-
X,Y,Z.
1. .
-
- X,Y
.
, ( -
):
N=1 Xmin Ymin 1 -1 -1
" 2 Xmax Ymin 1 1 -1
" 3 Xmin Ymax 1 -1 1
" 4 Xmax Ymax 1 1 1
, :
F=b0+b1*x1+b2*x2+b3*x3+b12*x1*x2;
x1=(X-z1)/dz1; x2=(Y-z2)/dz2;
z1:=(Xmax+Xmin)/2; dz1:=(Xmax-Xmin)/2;
z2:=(Ymax+Ymin)/2;
dz2:=(Ymax-Ymin)/2;
:
F=a0+a1*X+a2*Y+a3*Z+a12(X-z1)(Y-z2);
, -
|
|
- 2 -
12. -
:
F=c0+c1*X+(c2+c4*X)*Y+(c3+c5*Y+c6*X)*Z;
b12,a12,4,5,6=0, -
" ",
b1,b2.
2.
1.
X,Y .
2. "" -
.
y1..y4. "" .
3. -
.
4. : -
, "-
",
5. ,
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b - -
k .
6. -
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X,Y .
, F
.
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.
- 3 -
3. o .
,
- , , -
.
o -
.
5
" "
" ".
-
X,Y,Z.
1. .
- X,Y,Z
. -
, :
N=1 Xmin Ymin Zmin 1 -1 -1 -1
" 2 Xmax Ymin Zmin 1 1 -1 -1
" 3 Xmin Ymax Zmin 1 -1 1 -1
" 4 Xmax Ymax Zmin 1 1 1 -1
" 5 Xmin Ymin Zmax 1 -1 -1 1
" 6 Xmax Ymin Zmax 1 1 -1 1
" 7 Xmin Ymax Zmax 1 -1 1 1
" 8 Xmax Ymax Zmax 1 1 1 1
-
, :
F=b0+b1*x1+b2*x2+b3*x3+b12*x1*x2+b13*x1*x3+b23*x2*x3+b123*x1*x2*x3;
x1=(X-z1)/dz1; x2=(Y-z2)/dz2; x3=(Z-z3)/dz3)
z1:=(Xmax+Xmin)/2; dz1:=(Xmax-Xmin)/2; z2:=(Ymax+Ymin)/2;
dz2:=(Ymax-Ymin)/2; z3:=(Zmax+Zmin)/2;dz3:=(Zmax-Zmin)/2;
:
F=a0+a1*X+a2*Y+a3*Z+a12(X-z1)(Y-z2)+a13*(X-z1)(Z-z3)+
+a23*(Y-z2)*(Z-z3)+a123*(X-z1)(Y-z2)(Z-z3);
- 2 -
, 123.
:
F=c0+c1*X+(c2+c4*X)*Y+(c3+c5*Y+c6*X)*Z;
4,5,6=0,
" ",
1,2,3.
|
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2.
1.
X,Y,Z .
2. "" -
- .
F1..F8. "" -
.
3. -
. .
4. : -
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5. ,
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b - -
k .
6. -
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X,Y,Z .
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o -
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