×èñëåííûå ìåòîäû ðåøåíèÿ ñèñòåì ëèíåéíûõ óðàâíåíèé
End
Begin VB.TextBox
txtA11
Alignment
= 2 'Âûðàâíèâàíèå ïî Öåíòðó
BeginProperty
DataFormat
Type = 1
Format = "0,0000"
HaveTrueFalseNull= 0
FirstDayOfWeek = 0
FirstWeekOfYear = 0
LCID = 1049
SubFormatType
= 1
EndProperty
BeginProperty
Font
Name = "Times New Roman"
Size = 14.25
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 375
Left
= 600
TabIndex
= 7
Top
= 1440
Width
= 1095
End
Begin VB.Line Ñòðîêà3
X1
= 5760
X2
= 5760
Y1
= 1080
Y2
= 3360
End
Begin VB.Label Ìåòêà29
Caption
= "Z"
BeginProperty
Font
Name =
"Times New Roman"
Size = 12
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 255
Left
= 4920
TabIndex
= 36
Top
= 1080
Width
= 255
End
Begin VB.Label Ìåòêà28
Caption
= "Y"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 255
Left
= 3000
TabIndex
= 35
Top
= 1080
Width
= 255
End
Begin VB.Label Ìåòêà27
Caption
= "X"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough
= 0 'False
EndProperty
Height
= 375
Left
= 1080
TabIndex
= 34
Top
= 1080
Width
= 255
End
Begin VB.Label Ìåòêà23
Caption =
"Z"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 255
Left
= 4440
TabIndex
= 33
Top
= 3480
Width
= 255
End
Begin VB.Label Ìåòêà22
Caption
= "Y"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset = 204
Weight = 700
Underline = 0 'False
Italic
= 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 255
Left
= 3120
TabIndex
= 32
Top
= 3480
Width
= 255
End
Begin VB.Label Ìåòêà21
Caption
= "X"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 255
Left
= 1800
TabIndex
= 31
Top
= 3480
Width
= 255
End
Begin VB.Label Ìåòêà20
Caption
= "À33"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 375
Left
= 3840
TabIndex
= 27
Top
= 2640
Width
= 375
End
Begin VB.Label Ìåòêà19
Caption
= "À23"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 375
Left
= 3840
TabIndex
= 26
Top
= 2040
Width
= 375
End
Begin VB.Label Ìåòêà18
Caption
= "À13"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset = 204
Weight =
700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 375
Left
= 3840
TabIndex
= 25
Top =
1440
Width
= 375
End
Begin VB.Label Ìåòêà17
Caption
= "À32"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 375
Left
= 1920
TabIndex
= 21
Top
= 2640
Width
= 375
End
Begin VB.Label Ìåòêà16
Caption
= "À22"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset =
204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 375
Left
= 1920
TabIndex
= 20
Top
= 2040
Width
= 375
End
Begin VB.Label Ìåòêà15
Caption
= "À12"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 375
Left =
1920
TabIndex
= 19
Top
= 1440
Width
= 375
End
Begin VB.Line Ñòðîêà2
X1
= 0
X2
= 7800
Y1
= 3360
Y2
= 3360
End
Begin VB.Label Ìåòêà12
Alignment = 2
'Âûðàâíèâàíèå ïî Öåíòðó
Caption = "Ìåòîä îáðàòíîé ìàòðèöû"
BeginProperty Font
Name = "Times New Roman"
Size =
11.25
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 855
Left
= 0
TabIndex
= 15
Top
= 5280
Width
= 1095
End
Begin VB.Label Ìåòêà11
Alignment = 2
'Âûðàâíèâàíèå ïî Öåíòðó
Caption = "Ìåòîä Ãàóññà"
BeginProperty Font
Name = "Times New Roman"
Size = 11.25
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 615
Left
= 0
TabIndex
= 14
Top
= 4560
Width
= 1095
End
Begin VB.Label Ìåòêà10
Alignment = 2
'Âûðàâíèâàíèå ïî Öåíòðó
Caption = "Ìåòîä Êðàìåðà"
BeginProperty Font
Name = "Times New Roman"
Size = 11.25
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 615
Left
= 0
TabIndex
= 13
Top
= 3840
Width
= 1095
End
Begin VB.Label Ìåòêà7
Caption
= "Â3"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 375
Left
= 6000
TabIndex =
6
Top
= 2640
Width
= 255
End
Begin VB.Label Ìåòêà6
Caption
= "Â2"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset
= 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 375
Left
= 6000
TabIndex
= 5
Top
= 2040
Width
= 255
End
Begin VB.Label Ìåòêà5
Caption
= "Â1"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 375
Left =
6000
TabIndex
= 4
Top
= 1440
Width
= 255
End
Begin VB.Label Ìåòêà4
Caption
= "À31"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height =
375
Left
= 0
TabIndex
= 3
Top
= 2640
Width
= 375
End
Begin VB.Label Ìåòêà3
Caption
= "À21"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 375
Left
= 0
TabIndex
= 2
Top
= 2040
Width
= 375
End
Begin VB.Label Ìåòêà2
Caption
= "À11"
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 375
Left
= 0
TabIndex
= 1
Top
= 1440
Width
= 375
End
Begin VB.Label Ìåòêà1
Caption
= $"frmSlay.frx":0000
BeginProperty
Font
Name = "Times New Roman"
Size = 12
Charset = 204
Weight = 700
Underline = 0 'False
Italic = 0 'False
Strikethrough = 0 'False
EndProperty
Height
= 855
Left
= 120
TabIndex
= 0
Top
= 120
Width
= 7575
End
End
Attribute VB_Name =
"frmAriel"
Attribute
VB_GlobalNameSpace = False
Attribute VB_Creatable
= False
Attribute
VB_PredeclaredId = True
Attribute VB_Exposed =
False
Private Sub
cmdClean_Click()
Dim ñ As Byte
ñ =
MsgBox("Õîòèòå î÷èñòèòü?", 33, "Î÷èñòêà")
If ñ = 1 Then
txtA11.Text =
""
txtA12.Text =
""
txtA13.Text =
""
txtA21.Text =
""
txtA22.Text =
""
txtA23.Text =
""
txtA31.Text =
""
txtA32.Text =
""
txtA33.Text =
""
txtB1.Text =
""
txtB2.Text =
""
txtB3.Text =
""
txtMKX.Text =
""
txtMGX.Text =
""
txtMOMX.Text =
""
txtMKY.Text =
""
txtMGY.Text =
""
txtMOMY.Text =
""
txtMKZ.Text =
""
txtMGZ.Text =
""
txtMOMZ.Text =
""
End If
End Sub
Private Sub
cmdCount_Click()
If (Val(txtA11) *
Val(txtA22) * Val(txtA33) + Val(txtA12) * Val(txtA23) * Val(txtA31) +
Val(txtA21) * Val(txtA32) * Val(txtA13) - Val(txtA13) * Val(txtA22) *
Val(txtA31) - Val(txtA12) * Val(txtA21) * Val(txtA33) - Val(txtA23) *
Val(txtA32) * Val(txtA11)) = 0 Then
Dim g As Byte
g =
MsgBox("Ðåøèòü äàííóþ ñèñòåìó ìåòîäîì Êðàìåðà è ìåòîäîì îáðàòíîé ìàòðèöû
íåâîçìîæíî", 32, "Îïðåäåëèòåëü ñèñòåìû ðàâåí 0")
Else
ds = (Val(txtA11) *
Val(txtA22) * Val(txtA33) + Val(txtA12) * Val(txtA23) * Val(txtA31) +
Val(txtA21) * Val(txtA32) * Val(txtA13) - Val(txtA13) * Val(txtA22) *
Val(txtA31) - Val(txtA12) * Val(txtA21) * Val(txtA33) - Val(txtA23) *
Val(txtA32) * Val(txtA11))
dx = (Val(txtB1) *
Val(txtA22) * Val(txtA33) + Val(txtA12) * Val(txtA23) * Val(txtB3) + Val(txtB2)
* Val(txtA32) * Val(txtA13) - Val(txtA13) * Val(txtA22) * Val(txtB3) -
Val(txtA12) * Val(txtB2) * Val(txtA33) - Val(txtA23) * Val(txtA32) *
Val(txtB1))
dy = (Val(txtA11) *
Val(txtB2) * Val(txtA33) + Val(txtB1) * Val(txtA23) * Val(txtA31) + Val(txtA21)
* Val(txtB3) * Val(txtA13) - Val(txtA13) * Val(txtB2) * Val(txtA31) -
Val(txtB1) * Val(txtA21) * Val(txtA33) - Val(txtA23) * Val(txtB3) *
Val(txtA11))
dz = (Val(txtA11) *
Val(txtA22) * Val(txtB3) + Val(txtA12) * Val(txtB2) * Val(txtA31) + Val(txtA21)
* Val(txtA32) * Val(txtB1) - Val(txtB1) * Val(txtA22) * Val(txtA31) -
Val(txtA12) * Val(txtA21) * Val(txtB3) - Val(txtB2) * Val(txtA32) *
Val(txtA11))
txtMKX.Text = (dx /
ds)
txtMKY.Text = (dy /
ds)
txtMKZ.Text = (dz /
ds)
txtMOMX.Text =
(((Val(txtA22) * Val(txtA33) - Val(txtA23) * Val(txtA32)) / ds) * Val(txtB1) +
((Val(txtA13) * Val(txtA32) - Val(txtA12) * Val(txtA33)) / ds) * Val(txtB2) +
((Val(txtA12) * Val(txtA23) - Val(txtA13) * Val(txtA22)) / ds) * Val(txtB3))
txtMOMY.Text =
(((Val(txtA23) * Val(txtA31) - Val(txtA21) * Val(txtA33)) / ds) * Val(txtB1) +
((Val(txtA11) * Val(txtA33) - Val(txtA13) * Val(txtA31)) / ds) * Val(txtB2) +
((Val(txtA13) * Val(txtA21) - Val(txtA11) * Val(txtA23)) / ds) * Val(txtB3))
txtMOMZ.Text =
(((Val(txtA21) * Val(txtA32) - Val(txtA22) * Val(txtA31)) / ds) * Val(txtB1) +
((Val(txtA12) * Val(txtA31) - Val(txtA11) * Val(txtA32)) / ds) * Val(txtB2) +
((Val(txtA11) * Val(txtA22) - Val(txtA12) * Val(txtA21)) / ds) * Val(txtB3))
End If
If Val(txtA11) = 0
Then
Dim gg As Byte
gg =
MsgBox("Ðåøèòü äàííóþ ñèñòåìó ìåòîäîì Ãàóññà íåâîçìîæíî. Ïîìåíÿéòå
óðàâíåíèÿ ìåñòàìè, è ïîïðîáóéòå ñíîâà", 48, "Êîýôôèöèåíò ïðè õ â
ïåðâîì óðàâíåíèè ðàâåí 0")
Else
s1 = ((Val(txtB3) *
Val(txtA11)) - (Val(txtB1) * Val(txtA31)))
s2 = ((Val(txtA22) *
Val(txtA11)) - (Val(txtA12) * Val(txtA21)))
s3 = ((Val(txtB2) *
Val(txtA11)) - (Val(txtB1) * Val(txtA21)))
s4 = ((Val(txtA32) *
Val(txtA11)) - (Val(txtA12) * Val(txtA31)))
s5 = ((Val(txtA33) *
Val(txtA11)) - (Val(txtA12) * Val(txtA31)))
s6 = s2
s7 = ((Val(txtA23) *
Val(txtA11)) - (Val(txtA13) * Val(txtA21)))
s8 = s4
s12 = s1 * s2
s34 = s3 * s4
s56 = s5 * s6
s78 = s7 * s8
sh = s12 - s34
sz = s56 - s78
If sz = 0 Then
Dim ñ As Byte
ñ =
MsgBox("Äåëèòü íà íîëü íåëüçÿ.", 48, "Îøèáêà")
Else
txtMGZ.Text = (sh /
sz)
End If
sy1 = s3
sy2 = s2
sy3 = ((Val(txtA23) *
Val(txtA11)) - (Val(txtA13) * Val(txtA21)))
sy4 = s2
sy12 = (sy1) / (sy2)
sy34 = (sy3) / (sy4)
txtMGY.Text = ((sy12)
- ((sy34) * (sh / sz)))
sx1 = ((Val(txtB1)) /
(Val(txtA11)))
sx2 = ((Val(txtA13)) /
(Val(txtA11)))
sx3 = ((Val(txtA12)) /
(Val(txtA11)))
txtMGX.Text = ((sx1) -
((sx2) * (sh / sz)) - ((sx3) * ((sy12) - ((sy34) * (sh / sz)))))
End If
End Sub
Private Sub
cmdExit_Click()
Dim a As Byte
a = MsgBox("Õîòèòå âûéòè?", 33, "Âûõîä")
If a = 1 Then
End
End If
End Sub
Ïîëüçà
ââåäåíèÿ ðàñ÷åòîâ.
Îãðîìíîå
êîëè÷åñòâî ÷èñëåííûõ ìåòîäîâ ñòàâèò àêòóàëüíîé çàäà÷åé íå ñòîëüêî ñîçäàíèå
íîâûõ, ñêîëüêî èññëåäîâàíèå è êëàññèôèêàöèþ ñòàðûõ, âûÿâëåíèå ëó÷øèõ. Àíàëèç
âëèÿíèÿ îøèáîê ïîêàçàë, ÷òî ìåæäó ëó÷øèìè ìåòîäàìè íåò ïðèíöèïèàëüíîé ðàçíèöû ñ
òî÷êè çðåíèÿ óñòîé÷èâîñòè ê îøèáêàì îêðóãëåíèÿ. Ñîçäàíèå ìîùíûõ êîìïüþòåðîâ
ñóùåñòâåííî îñëàáèëî çíà÷åíèå ðàçëè÷èÿ ìåæäó ìåòîäàìè (â òàêèõ õàðàêòåðèñòèêàõ,
êàê îáú¸ì òðåáóåìîé ïàìÿòè, êîëè÷åñòâî àðèôìåòè÷åñêèõ îïåðàöèé).  ýòèõ óñëîâèÿ
íàèáîëåå ïðåäïî÷òèòåëüíûìè ñòàíîâÿòñÿ òå ìåòîäû, êîòîðûå íå î÷åíü îòëè÷àþòñÿ îò
ëó÷øèõ ïî ñêîðîñòè è óäîáñòâó ðåàëèçàöèè íà êîìïüþòåðàõ, ïîçâîëÿþò ðåøàòü
øèðîêèé êëàññ çàäà÷ êàê õîðîøî, òàê è ïëîõî îáóñëîâëåííûõ è äàâàòü ïðè ýòîì
îöåíêó òî÷íîñòè âû÷èñëèòåëüíîãî ðåøåíèÿ.
 MathCAD è Excel ÷èñëåííûå ìåòîäû ïðåäñòàâëÿþò ñîáîé òå æå ñàìûå îáùåïðèíÿòûå
ðó÷íûå ðàñ÷¸òû, íî âûïîëíÿåìûå íå ÷åëîâåêîì, à êîìïüþòåðîì, ÷òî ïîíèæàåò
âîçìîæíîñòü îøèáêè äî íóëÿ. Ïðîãðàììà íà Visual
Basic íàìíîãî óïðîùàåò çàäà÷ó. Ñ
ïîìîùüþ åäèíîæäû ñîçäàííîé ïðîãðàììû ìîæíî ðåøàòü ñèñòåìû ëèíåéíûõ óðàâíåíèé,
ââîäÿ ìèíèìóì çíà÷åíèé. Òàêæå ýòà ïðîãðàììà ìîæåò áûòü èñïîëüçîâàíà íå òîëüêî
âàìè, íî è ïðîñòûìè ïîëüçîâàòåëÿìè.
III.
Ëèòåðàòóðà
1) Ì. Äîäæ, Ê. Êèíàòà, Ê. Ñòèíñîí "Ýôôåêòèâíàÿ ðàáîòà â Microsoft Excel 97", èçäàòåëüñòâî "Ïèòåð"; Ñàíêò-Ïåòåðáóðã, 1998ã. 2) Å.Ê. Îâ÷àðåíêî, Î.Ï. Èëüèíà, Å.Â. Áàëûáåðäèí "Ôèíàíñîâî - ýêîíîìè÷åñêèå ðàñ÷åòû â Excel", Ìîñêâà, 1999 ã. 3) Éîðã Øèá, Excel 7,0: Ñîòíè ïîëåçíûõ ðåöåïòîâ, Äþññåëüäîðô-Êèåâ-Ìîñêâà- Ñàíêò-Ïåòåðáóðã, 1997 ã.
4) Ñèìîíîâè÷ Ñ.Â. è äð. Èíôîðìàòèêà
Áàçîâûé êóðñ: Ó÷åá, äëÿ òåõíè÷åñêèõ âóçîâ. ÑÏÁ: Èçä. «Ïèòåð», 2004.–640ñ
5) Êàëèòêèí Í.Í. è äð. ×èñëåííûå
ìåòîäû. Ì.: Íàóêà, 1982
6) Òóð÷àê Ë.È. Îñíîâû ÷èñëåííûõ
ìåòîäîâ. Ì.: Íàóêà, 1987
7) Äüÿêîíîâ Â.Ï. Ñèñòåìà MathCAD. Ì.: Ðàäèî è ñâÿçü, 1993
Ñòðàíèöû: 1, 2, 3, 4, 5, 6
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