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:

































 

 

 

 


-

:

. 411171

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: . .

..

 

 

, 2012


1. . 3

. 3

:

() .. 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
A10:C12
0,3

4,3 1,5 -2,3
6,5 -2,5 3,2
     
0,5 -0,24
A14:C16
0,3

1,6 4,3 -2,3
3,7 6,5 3,2
     
0,5 1,7
A18:20
-0,24

1,6 1,5 4,3
3,7 -2,5 6,5

) ∆, ∆1, ∆2, ∆3 (∆ ) =(A1:C3):

=(A1:C3)


=(A10:C12)
-26,511

1
=(A14:C16)
-54,729

2
=(A18:C20)
15,9732

3 21,909

 

) 1/, 2/, 3/.

 

3) :

) . .

) . .

n- .

: a(n,n)- ; b(n)- ( ); x(n)- .

,
n, a, b

FOR k=1 TO n-1
,

FOR i=k+1 TO n
m=aik/akk

FOR j=k+1 TO n
aij=aij-m*akj
bi=bi-m*bk
xn=bn/ann
FOR i=n-1 TO 1 - 1

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  
-
             

 

, . .

, - - .

5 : , , , -. 3 . , , . , , ( ), . , . , . ( ) 0 . , , .

- ( ). - , . .. . . , . 255, 234 -, , .

, , , . , , .

 

 

 

 

1. ..

2. .. . Excel: . 2. / . . . -; , 2003, . 72

3. .., .. : . .: , 2001.-256 :.

4. .. . / . . . ; ,2007, 112 .

5. .. . - .: , 1987. 318 .

6. .. : . .: .1989. 240 .

7. .., .. MS Visual Basic: / . .. . .: , 2001. 320 .: .

 

 



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