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. 411171
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, 2012
1. . 3
. 3
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() .. 3-4
.. 5
. 4
.. 5
.. 5
.. 5
2. ɻ
:
A1:C3;E1:E3
0,5 | 1,7 | 0,3 | -0,24 | |
1,6 | 1,5 | -2,3 | 4,3 | |
3,7 | -2,5 | 3,2 | 6,5 |
0,51+1,72+0,33=-0,24
1,61+1,52-2,33=4,3
3,71-2,52+3,23=6,5
:
1. ,
2. ,
3. ,
4. ,
5. -.
:
()
1) : ( =-1* , - , -1- )
) =(1:3) :
0,035834 | 0,233488 | 0,16446 |
0,514126 | -0,01848 | -0,06148 |
0,360228 | -0,28441 | 0,074309 |
) =(A5:C7;E1:E3).
2) : (xi=∆i/∆, ∆- , ∆i-, i- ):
) :
-0,24 | 1,7 |
| |
4,3 | 1,5 | -2,3 | |
6,5 | -2,5 | 3,2 | |
0,5 | -0,24 |
| |
1,6 | 4,3 | -2,3 | |
3,7 | 6,5 | 3,2 | |
0,5 | 1,7 |
| |
1,6 | 1,5 | 4,3 | |
3,7 | -2,5 | 6,5 |
) ∆, ∆1, ∆2, ∆3 (∆ ) =(A1:C3):
=(A1:C3) |
| ||
1 |
| |
2 |
| |
3 | 21,909 |
) 1/, 2/, 3/.
3) :
) . .
) . .
n- .
: a(n,n)- ; b(n)- ( ); x(n)- .
| |||
FOR k=1 TO n-1 | |||
| |||
FOR i=k+1 TO n | |||
FOR j=k+1 TO n | |||
aij=aij-m*akj | |||
bi=bi-m*bk | |||
xn=bn/ann | |||
| |||
FOR j=i+1 TO n | |||
S=∑aij*xi | |||
xi=(bi-s)/aii | |||
xi |
, . .- |
g=k |
FOR i=k+1 TO n |
|aik|>|agk|, g=i |
FOR j=k TO n |
z=agj; agj=akj; akj=z |
z=bg; bg=bk;bk=z |
, > = :
3,7 | -2,5 | 3,2 | 6,5 | |
0,5 | 1,7 | 0,3 | -0,24 | |
1,6 | 1,5 | -2,3 | 4,3 |
1) :
) 1, 2, 3 , :
x1=(b1-a12x2-a13x3)/a11
x2=(b2-a21x1-a23x3)/a22
x3=(b3-a31x1-a32x2)/a33
) () x1(0), x2(0), x3(0) . , .
) k- , n :
xi(k)= (k-1))
,
|xi(k)-xi(k-1)|<e, i=1,2, n.
, , xi(k-1)= xi(k)
2) -:
, k- j<i xi , :
xi(k)= (k)- (k-1))
,
|xi(k)-xi(k-1)|<e, i=1,2, n.
, , xi(k-1)= xi(k)
-
n, e, a, b, x |
FOR i=1 TO n |
FOR j=1 TO n |
S= |
Xk=(bi-s)/aii |
S1= |
Xi=xk |
, s1<e |
xi |
n- ; e-; a(n,n)- ; b(n)- ; x(n)- . x(n).
Visual Basic ( Visual Basic, ) [1].
Sub metod_g()
n = 3
Dim a(1 To 3, 1 To 3)
Dim b(1 To 3)
Dim x(1 To 3)
For i = 1 To 3
For j = 1 To 3
a(i, j) = Worksheets("2").Cells(i, j).Value
Next j
Next i
For i = 1 To 3
b(i) = Worksheets("2").Cells(i, 5).Value
Next i
For k = 1 To n - 1
g = k
For i = k + 1 To n
If Abs(a(i, k)) > Abs(a(g, k)) Then g = i
Next i
For j = k To n
z = a(g, j): a(g, j) = a(k, j): a(k, j) = z
Next j
z = b(g): b(g) = b(k): b(k) = z
For i = k + 1 To n
m = a(i, k) / a(k, k)
For j = k + 1 To n
a(i, j) = a(i, j) - m * a(k, j)
Next j
b(i) = b(i) - m * b(k)
Next i
Next k
x(n) = b(n) / a(n, n)
For i = n - 1 To 1 Step -1
s = 0
For j = i + 1 To n
s = s + a(i, j) * x(j)
Next j
x(i) = (b(i) - s) / a(i, i)
Next i
For i = 1 To 3
Worksheets("2").Cells(i, 9).Value = x(i)
|
|
Next i
End Sub
Sub MPI_SLAY()
n = 3
e = 0.0001
Dim a(1 To 3, 1 To 3)
Dim b(1 To 3)
For i = 1 To 3
For j = 1 To 3
a(i, j) = Worksheets("3").Cells(i, j).Value
Next j: Next i
For i = 1 To 3
b(i) = Worksheets("3").Cells(i, 5).Value
Next i
x10 = 0
x20 = 0
x30 = 0
Do
x1 = (b(1) - a(1, 2) * x20 - a(1, 3) * x30) / a(1, 1)
x2 = (b(2) - a(2, 1) * x10 - a(2, 3) * x30) / a(2, 2)
x3 = (b(3) - a(3, 1) * x10 - a(3, 2) * x20) / a(3, 3)
c = Abs(x1 - x10) + Abs(x2 - x20) + Abs(x3 - x30)
x10 = x1
x20 = x2
x30 = x3
k = k + 1
Loop While c > e
With Worksheets("2")
.Range("J1").Value = x1
.Range("J2").Value = x2
.Range("J3").Value = x3
.Range("J5").Value = k
End With
End Sub
Sub GausZeid()
n = 3
e = 0.0001
Dim a(1 To 3, 1 To 3)
Dim b(1 To 3)
For i = 1 To 3
For j = 1 To 3
a(i, j) = Worksheets("3").Cells(i, j).Value
b(i) = Worksheets("3").Cells(i, 5).Value
Next j
Next i
x10 = 0: x20 = 0: x30 = 0
k = 0
Do
x1 = (b(1) - a(1, 2) * x20 - a(1, 3) * x30) / a(1, 1)
x2 = (b(2) - a(2, 1) * x1 - a(2, 3) * x30) / a(2, 2)
x3 = (b(3) - a(3, 1) * x1 - a(3, 2) * x2) / a(3, 3)
c = Abs(x1 - x10) + Abs(x2 - x20) + Abs(x3 - x30)
x10 = x1
x20 = x2
x30 = x3
k = k + 1
Loop While c > e
With Worksheets("2")
.Range("K1").Value = x1
Range("K2").Value = x2
.Range("K3").Value = x3
.Range("K5").Value = k
End With
End Sub
Run.
2.
x1 | 2,064388 | 2,064388 | 2,064388 | 2,064429 | 2,064371 | |
x2 | -0,60251 | -0,60251 | -0,60251 | -0,60252 | -0,60251 | |
x3 | -0,82641 | -0,82641 | -0,82641 | -0,82638 | -0,82642 | |
- | ||||||
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1. ..
2. .. . Excel: . 2. / . . . -; , 2003, . 72
3. .., .. : . .: , 2001.-256 :.
4. .. . / . . . ; ,2007, 112 .
5. .. . - .: , 1987. 318 .
6. .. : . .: .1989. 240 .
7. .., .. MS Visual Basic: / . .. . .: , 2001. 320 .: .