数值计算编程20个

1、1、P11，第一题Private Sub Form_Click()Dim a, b, x, s As Doublea = 1b = 2s = 0.001Dox = (a + b) / 2If (x 3 - x - 1) * (a 3 - a - 1) 0 Thenb = xElsea = xEnd IfLoop Until Abs(x 3 - x - 1) sPrint xPrint x 3 - x - 1End Sub结果：1.324707031252、P12，第五题Private Sub Form_Click()Dim a, x, s As Doublea = 8s = 0.001x =

2、aDop = xx = (p + a / p) / 2Loop Until Abs(x - p) sPrint xEnd Sub结果：2.828427125049863、程序：Private Sub Form_Click()Dim i As IntegerDim t, a(0 To 3), p As Doublet = 2For i = 0 To 3a(i) = InputBox(x( & i & )=)Next ip = a(3)For i = 2 To 0 Step -1p = p * t + a(i)Next iPrint pEnd Sub结果：494、程序：Private Sub Fo

3、rm_Click()Dim a, b, s As Doublea = 0.2b = 1.34s = (a + b) / 2DoIf a * (1 - a) * s * (1 - s) 0 Thenb = sElsea = sEnd Ifs = (a + b) / 2Loop Until b - a 0.01Print sEnd Sub结果：0.9971093755、程序：Private Sub Form_click()Dim x, s, p As DoubleDim i As Integerx = 101s = 10p = 1 / 2 / 10i = 1Dos = s + pp = p / 2

4、 * (-1) / 100 * (2 * i - 1)i = i + 1Loop Until p 0.01Print sEnd Sub结果：10.056、拉格朗日：Private Sub Form_Click()Dim i, j, n As IntegerDim x(1 To 100), y(1 To 100), p, s, t As Doublet = 2.5n = 3For i = 1 To nx(i) = InputBox(x( & i & )=)y(i) = InputBox(y( & i & )=)Next is = 0For i = 1 To np = 1For j = 1 To

5、nIf i j Thenp = p * (t - x(j) / (x(i) - x(j)End IfNext js = s + p * y(i)Next iPrint sEnd Sub结果：67、课堂埃尔米特插值程序：Private Sub Form_Activate()Dim x0, y0, x1, y1, g0, g1 As Doublex0 = 0y0 = 0x1 = 1y1 = 1g0 = 0g1 = 2x = 0.5a0 = -2 / (x0 - x1) 3b0 = 1 / (x0 - x1) 2 + 2 * x0 / (x0 - x1) 3a1 = -2 / (x1 - x0) 3

6、b1 = 2 * x1 / (x1 - x0) 3 + 1 / (x1 - x0) 2k0 = 1 / (x0 - x1) 2k1 = 1 / (x1 - x0) 2l0 = (x - x1) 2 * (a0 * x + b0)l1 = (x - x0) 2 * (a1 * x + b1)gg0 = k0 * (x - x0) * (x - x1) 2gg1 = k1 * (x - x0) 2 * (x - x1)y = l0 * y0 + l1 * y1 + gg0 * g0 + gg1 * g1Print yEnd Sub结果：0.258、第一个：样条函数：Private Sub Form

7、_Activate()Dim x(3), y(3), m0, m1, m2 As DoubleDim i As IntegerFor i = 0 To 2x(i) = iy(i) = i * iNext im0 = 0m2 = 4h0 = x(1) - x(0)h1 = x(2) - x(1)a = 2 / h0b = 4 / h0 + 4 / h1c = 2 / h1d = (-6 * y(1) + 6 * y(2) / h1 2 - (6 * y(0) - 6 * y(1) / h0 2m1 = (d - a * m0 - c * m2) / bPrint m1End Sub结果：29、牛

8、顿插值：Dim k As IntegerPrivate Sub Combo1_Click()Dim i As Integerk = CInt(Combo1.Text)For i = 0 To 9Text1(2 * i).Visible = FalseText1(2 * i + 1).Visible = FalseLabel(i).Visible = FalseNext iFor i = 0 To k - 1With Label(i).Visible = True.Top = 1560 + 400 * i.Caption = 第 & i + 1 & 点：.Left = 120End WithWi

9、th Text1(2 * i).Visible = True.Left = 800.Top = 1500 + 400 * iEnd WithWith Text1(2 * i + 1).Visible = True.Left = 1500.Top = 1500 + 400 * iEnd WithNext iEnd SubPrivate Sub Command1_Click()Dim i As IntegerDim s As Doubles = 0For i = 0 To k - 1s = s + ff(i) * f1(Text3.Text, i)Next iText2.Text = sEnd S

10、ubPrivate Sub Command2_Click()EndEnd SubPrivate Sub Form_Load()Dim i As IntegerFor i = 2 To 10Combo1.AddItem iNext iEnd SubFunction ff(ByVal n As Integer)Dim i As IntegerDim s As Doubles = 0If n = 0 Thenff = Text1(1).TextExit FunctionEnd IfFor i = 0 To ns = s + Text1(2 * i + 1).Text / f(i, n)Next if

11、f = sEnd FunctionFunction f(ByVal p As Integer, ByVal n As Integer)Dim i As IntegerDim s As Doubles = 1For i = 0 To nIf i p Thens = s * (Text1(2 * p).Text - Text1(2 * i).Text)End IfNext if = sEnd FunctionFunction f1(ByVal x As Double, ByVal n As Integer)Dim i As IntegerDim s As DoubleIf n = 0 Thenf1

12、 = 1Exit FunctionEnd Ifs = 1For i = 0 To n - 1s = s * (x - Text1(2 * i).Text)Next if1 = sEnd Function结果：带入（1,1），（2,4），（3,7），（4,8），（5,6）得到变量为3.5时，插值结果为7.835937510、复化辛普生算法：Private Sub Command1_Click()Dim i, n As IntegerDim s, h, x As Doublea = InputBox(请输入左端点a：)b = InputBox(请输入右端点b：)n = InputBox(请输入分段

13、数n：)h = (b - a) / ns = f(b) - f(a)x = aFor i = 1 To nx = x + h / 2s = s + 4 * f(x)x = x + h / 2s = s + 2 * f(x)Next is = h / 6 * sText1.Text = sEnd SubFunction f(ByVal x As Double)If x = 0 Thenf = 1Exit FunctionEnd Iff = Sin(x) / xEnd Function结果：当输入区间为（0,1），分8段，运行结果是0.93947770975194311、p153 第6题Priva

14、te Sub Form_Load()Dim s, t, e As DoubleDim i, k As Integert = 0k = 0s = (t + 2) 0.5e = 0.001For i = 0 To 20If Abs(s - t) e Thenk = 1Exit ForEnd Ift = ss = (t + 2) 0.5Next iText1.Text = sEnd Sub结果：1.9998494036782912、p154 第18题Dim a As DoublePrivate Sub Form_Load()Dim x0, x, e As DoubleDim i As Integer

15、x = 5e = 0.000001a = InputBox(a=)For i = 0 To 20x0 = xText1.Text = Text1.Text & vbCrLf & f1(x0)If f1(x0) = 0 ThenExit ForEnd Ifx = x0 - f(x0) / f1(x0)If Abs(x - x0) e ThenExit ForEnd IfNext iIf i = 20 ThenMsgBox 迭代失败！EndEnd IfText1.Text = xEnd SubFunction f(ByVal x As Double)f = x 3 - aEnd FunctionF

16、unction f1(ByVal x As Double)f1 = 3 * x 2End Function结果：2.1544346900318813、p155 第24题牛顿法Private Sub Form_Load()Dim x0, e As DoubleDim i As Integerx0 = 0e = 0.000001n = 20If f1(x0) = 0 ThenMsgBox 奇异EndEnd IfFor i = o To 20x0 = xIf f1(x) = 0 ThenMsgBox 奇异EndEnd Ifx = x0 - f(x0) / f1(x0)If Abs(x - x0) e

17、 ThenExit ForEnd IfNext iIf i = 20 ThenMsgBox 迭代失败！EndEnd IfText1.Text = xEnd SubFunction f(ByVal x As Double)f = x 3 + 2 * x 2 + 10 * x - 20End FunctionFunction f1(ByVal x As Double)f1 = 3 * x 2 + 4 * x + 10End Function结果：1.3688081078213714、p155 第24题弦截法Private Sub Form_Load()Dim x0, x1, e As Double

18、Dim i As Integerx0 = 0e = 0.000001n = 20If f1(x0) = 0 ThenMsgBox 奇异EndEnd Ifx1 = x0 - f(x0) / f1(x0)For i = o To 20x = x1 - f(x1) / (f(x1) - f(x0) * (x1 - x0)If Abs(x - x1) e ThenExit ForEnd Ifx1 = xNext iIf i = 20 ThenMsgBox 迭代失败！EndEnd IfText1.Text = xEnd SubFunction f(ByVal x As Double)f = x 3 +

19、2 * x 2 + 10 * x - 20End FunctionFunction f1(ByVal x As Double)f1 = 3 * x 2 + 4 * x + 10End Function结果：1.3688083714056215、p155 第24题快速弦截法Private Sub Form_Load()Dim x0, x1, e As DoubleDim i As Integerx0 = 0e = 0.000001n = 20If f1(x0) = 0 ThenMsgBox 奇异EndEnd Ifx1 = x0 - f(x0) / f1(x0)For i = o To 20x0

20、= x1x1 = xx = x1 - f(x1) / (f(x1) - f(x0) * (x1 - x0)If Abs(x - x1) e ThenExit ForEnd IfNext iIf i = 20 ThenMsgBox 迭代失败！EndEnd IfText1.Text = xEnd SubFunction f(ByVal x As Double)f = x 3 + 2 * x 2 + 10 * x - 20End FunctionFunction f1(ByVal x As Double)f1 = 3 * x 2 + 4 * x + 10End Function结果：1.368808

21、1077549616、消去法Dim n As IntegerDim a(1 To 10, 1 To 10), b(1 To 10), x(1 To 10) As DoublePrivate Sub Combo1_Click()Dim i, j As IntegerFor i = 1 To 100Text1(i).Visible = FalseNext iFor i = 1 To 10Text2(i).Visible = FalseText3(i).Visible = FalseNext in = Combo1.TextFor i = 1 To nFor j = 1 To nWith Text1

22、(i - 1) * n + j).Visible = True.Top = 500 * i + 200.Left = 500 * j.Height = 300End WithNext jWith Text2(i).Visible = True.Top = 500 * i + 200.Left = 500 * n + 800.Height = 300End WithWith Text3(i).Visible = True.Top = 500 * i + 200.Left = 500 * n + 1800.Width = 700.Height = 300End WithNext iEnd SubP

23、rivate Sub Command1_Click()Dim i, j, k As IntegerDim s, r As DoubleFor i = 1 To nFor j = 1 To na(i, j) = Text1(i - 1) * n + j).TextNext jb(i) = Text2(i).TextNext iFor i = 1 To n - 1For j = i + 1 To nr = a(j, i) / a(i, i)For k = i To na(j, k) = a(j, k) - r * a(i, k)Next kb(j) = b(j) - r * b(i)Next jN

24、ext iFor i = n To 1 Step -1s = b(i)If i n ThenFor j = i To ns = s - a(i, j) * x(j)Next jEnd Ifx(i) = s / a(i, i)Text3(i).Text = x(i)Next iEnd SubPrivate Sub Command2_Click()EndEnd SubPrivate Sub Form_Load()Dim i As IntegerFor i = 2 To 10Combo1.AddItem iNext iEnd Sub结果：选择求解未知数个数为3，再依次输入A=2，-1,3；4,2,5

25、；1,2,0；B=1,4,7；得到x=9，-1，-617、 追赶法Private Sub Command1_Click()Dim i, j, k As IntegerDim aa(1 To 4), bb(1 To 4), cc(1 To 4), dd(1 To 4), xx(1 To 4), g(1 To 4), f(1 To 4) As DoubleDim s, r As DoubleFor i = 1 To 4If i = 1 Thenaa(i) = 0Elseaa(i) = a(i).TextEnd Ifbb(i) = b(i).TextIf i = 4 Thencc(i) = 0Els

26、ecc(i) = c(i).TextEnd Ifdd(i) = d(i).TextNext ig(1) = dd(1) / bb(1)f(1) = -cc(1) / bb(1)For i = 2 To 4g(i) = (dd(i) - aa(i) * g(i - 1) / (aa(i) * f(i - 1) + bb(i)f(i) = -cc(i) / (aa(i) * f(i - 1) + bb(i)Next ixx(4) = g(4)x(4).Text = xx(4)For i = 3 To 1 Step -1xx(i) = g(i) + f(i) * xx(i + 1)x(i).Text

27、 = xx(i)Next iEnd SubPrivate Sub Command2_Click()EndEnd Sub结果：依次输入方程组系数A=1,1；1,2,1；1,2,3；1,2；，B=3,8,20,11得到结果为X=1,2,3,4；18、高斯-赛德尔程序如下：Private Sub Command1_Click()Dim i, j As IntegerDim k, t(1 To 3), s, a(1 To 3, 1 To 3), b(1 To 3), x(1 To 3) As DoubleFor i = 1 To 3For j = 1 To 3a(i, j) = Text1(i * 3

28、 + j - 3).TextNext jb(i) = Text2(i).Textx(i) = 0Next ik = 1Do Until k 0.0001For i = 1 To 3s = b(i)For j = 1 To 3If j i ThenText4.Text = ss = s - a(i, j) * x(j)Text5.Text = sEnd IfNext jt(i) = s / a(i, i)If i = 1 Thenk = Abs(t(i) - x(i)ElseIf Abs(t(i) - x(i) k Thenk = Abs(t(i) - x(i)End Ifx(i) = t(i)

29、Next iLoopFor i = 1 To 3Text3(i).Text = x(i)Next iEnd Sub运行结果:输入系数A=7,5,-3;5,7,1;2,1,7; B=2,4,-11得到X=-1.727,2.000,-1.36319、迭代法程序如下：Private Sub Command1_Click()Dim i, j As IntegerDim k, t(1 To 3), s, a(1 To 3, 1 To 3), b(1 To 3), x(1 To 3) As DoubleFor i = 1 To 3For j = 1 To 3a(i, j) = Text1(i * 3 + j - 3).TextNext jb(i) = Text2(i).Textx(i) = 0Next ik = 1Do Until k 0.0001For i = 1 To 3s = b(i)F