一次插值代码（插值处理实现）

今天给各位分享一次插值代码的知识，其中也会对插值处理实现进行解释，如果能碰巧解决你现在面临的问题，别忘了关注本站，现在开始吧！

本文目录一览：

• 1、100分求高手帮我写下牛顿插值和样条插值的VB代码，急用啊！！！
• 2、拉格朗日插值的matlab代码
• 3、如何用matlab实现插值算法
• 4、牛顿插值法，用VB写代码？
• 5、c++，求插值。。高分求。。。答好再加！！
• 6、谁有拉格朗日插值法的python代码啊！急用啊！谢谢啦！

100分求高手帮我写下牛顿插值和样条插值的VB代码，急用啊！！！

自编的，都弄上来了，缺样条插值。这里仅是函数，什么控件的编程你自己弄，那实在太简单了。

Dim aa As Double, bb As Double '分别接收findway有根区间两端值的变量

Dim x(1) As Double '分别接收ercigenway的根

'1.0 ercigenway 求二次方程实根 -已测试

Private Sub ercigenway(a As Single, b As Single, c As Single) 'a、b、c对应为二次方程的系数

Dim d As Double

d = b ^ 2 - 4 * a * c

If d 0 Then

MsgBox "Δ小于0，没有实根", , "消息"

x(0) = 0: x(1) = 0

ElseIf d = 0 Then

x(0) = -b / (2 * a): x(1) = x(0)

Else

x(0) = (-b - Sgn(b) * Sqr(d)) / (2 * a): x(1) = c / (a * x(0))

End If

End Sub

'2.1 findway 等步长扫描有根区间 -已测试

Private Sub findway(ByVal a As Single, ByVal b As Single, h As Double) 'a、b分别为待扫描区间端点，h为步长

Dim a1 As Double

a1 = a

Do

If f(a1) * f(a1 + h) = 0 Then

aa = a1: bb = a1 + h

Exit Sub

End If

a1 = a1 + h

Loop While a1 b

If a1 b Then

MsgBox "没有找到有根区间，请换更小的步长试一下"

Exit Sub

End If

End Sub

'2.2 erfenfun 二分法求根 -已测试

Private Function erfenfun(ByVal a As Single, ByVal b As Single, eps As Double) 'a、b为有根区间端点，eps为误差

Dim x0 As Double, x1 As Double, x2 As Double, f0 As Double, f1 As Double, f2 As Double

x1 = a: x2 = b

Do

x0 = (x1 + x2) / 2

f0 = f(x0)

If f0 = 0 Then

Exit Do

Else

f1 = f(x1): f2 = f(x2)

If f0 * f1 0 Then

x2 = x0

Else

x1 = x0

End If

End If

Loop While Abs(x1 - x2) eps

x0 = (x1 + x2) / 2

erfenfun = x0

End Function

'2.4 newtonfxfun Newton切线法 -已测试

Private Function newtonfxfun(ByVal x0 As Double, eps As Double) As Double 'x0为附近根，eps为误差

Dim x1 As Double, f0 As Double, f1 As Double

x1 = x0

Do

x0 = x1

f0 = f(x0): f1 = fd(x0) 'fd表示f的导函数

If Abs(f1) eps Then

x1 = x0: Exit Do

End If

x1 = x0 - f0 / f1

Loop Until Abs(x1 - x0) eps

newtonfxfun = x1

End Function

'2.3 stediedaifun Seffensen加速迭代法 (方程形式为x-f(x)=0) -已测试

Private Function stediedaifun(ByVal x0 As Double, eps1 As Double, eps2 As Double) As Double 'x0为解析解附近的根，eps1为输出结果误差，eps2为迭代能否继续判断标准

Dim y As Double, z As Double, x1 As Double

x1 = x0

Do

x0 = x1

y = f(x0): z = f(y)

If Abs(z - 2 * y + x0) eps2 Then

MsgBox "为满足eps2条件，不能继续迭代"

Exit Function

End If

x1 = x0 - (y - x0) ^ 2 / (z - 2 * y + x0)

Loop Until Abs(x1 - x0) eps1

stediedaifun = x1

End Function

'2.5 newtonfxnfun n次代数方程Newton切线法 -已测试

Private Function newtonfxnfun(a() As Single, eps As Double, x0 As Double) As Double 'a()分别存储按降幂排列的方程的n个系数，eps为误差，x0为附近根

Dim k As Integer, n As Integer, f0 As Double, f1 As Double, x1 As Double

n = UBound(a)

x1 = x0

Do

x0 = x1

f0 = a(0): f1 = f0

For k = 1 To n - 1

f0 = a(k) + f0 * x0

f1 = f0 + f1 * x0

Next k

f0 = a(n) + f0 * x0

x1 = x0 - f0 / f1

Loop Until Abs(x1 - x0) eps

newtonfxnfun = x1

End Function

'2.6 linecutfun 弦截法 -已测试

Private Function linecutfun(ByVal x0 As Double, ByVal x1 As Double, eps As Double, n As Long) As Double 'n为迭代次数限制，x0、x1为有根区间端点，eps为误差

Dim f0 As Double, f1 As Double, f2 As Double

Dim x2 As Double, i As Long

f0 = f(x0): f1 = f(x1)

For i = 1 To n

x2 = x1 - (x1 - x0) * f1 / (f1 - f0)

f2 = f(x2)

If Abs(f2) eps Then

Exit For

End If

x0 = x1: x1 = x2: f0 = f1: f1 = f2

Next i

If i = n + 1 Then

MsgBox "要求的计算次数太低，没有达到精度要求"

End If

linecutfun = x2

End Function

'4.1 lagrangeczfun 拉格朗日插值法 -已测试

Private Function lagrangeczfun(a() As Double, ByVal u As Double) As Double 'a(1,n)存储n+1个节点，u为插值点

Dim i As Integer, j As Integer, n As Integer

Dim l As Double, v As Double

v = 0

n = UBound(a, 2)

For j = 0 To n

l = 1#

For i = 0 To n

If i = j Then GoTo hulue

l = l * (u - a(0, i)) / (a(0, j) - a(0, i))

hulue:

Next i

v = v + l * a(1, j)

Next j

lagrangeczfun = v

End Function

'4.2 newtonczfun newton插值法 -已测试

Private Function newtonczfun(a() As Double, u As Double) As Double 'a(1,n)存储n+1个节点，u为插值点

Dim n As Integer, i As Integer, j As Integer, k As Integer

Dim z() As Double, f() As Double, v As Double

n = UBound(a, 2)

ReDim z(n), f(n)

For i = 0 To n

z(i) = a(1, i)

Next i

For i = 1 To n

k = k + 1

For j = i To n

f(j) = (z(j) - z(j - 1)) / (a(0, j) - a(0, j - k))

Next j

For j = i To n

z(j) = f(j)

Next j

Next i

f(0) = a(1, 0)

v = 0

For i = n To 0 Step -1

v = v * (u - a(0, i)) + f(i)

Next i

newtonczfun = v

End Function

'4.3 hermiteczfun Hermite插值法 -已测试

Private Function hermiteczfun(a() As Double, fd() As Double, u As Double) As Double 'a(1,n)存储n+1个节点，fd(n)存储n+1个节点处导数值，u为插值点

Dim l() As Double, ld() As Double, g() As Double, h() As Double, aim As Double

Dim n As Integer, i As Integer, j As Integer

n = UBound(a)

ReDim l(n), ld(n), g(n), h(n)

aim = 0

For i = 0 To n

l(i) = 1: ld(i) = 0

For j = 0 To n

If j = i Then GoTo hulue

l(i) = l(i) * (u - a(0, j)) / (a(0, i) - a(0, j))

ld(i) = ld(i) + 1 / (a(0, i) - a(0, j))

hulue:

Next j

g(i) = (1 + 2 * (a(0, i) - u) * ld(i)) * l(i) * l(i)

h(i) = (u - a(0, i)) * l(i) * l(i)

aim = aim + g(i) * a(1, i) + h(i) * fd(i)

Next i

hermiteczfun = aim

End Function

'5.2.1 tixingjffun 变步长梯形积分法 -已测试

Private Function tixingjffun(a As Single, b As Single, eps As Double, m As Long) As Double 'a、b分别为积分上下限，eps为误差，m为最大计算次数

Dim h As Double, t1 As Double, t2 As Double, t As Double, hh As Double

Dim n As Long: n = 1

h = b - a: t1 = h * (f(a) + f(b)) / 2

Do

t = 0

For i = 1 To n

t = t + f(a + (i - 0.5) * h)

Next i

hh = h * t

t2 = (t1 + hh) / 2

If Abs(t2 - t1) eps Then Exit Do

t1 = t2: h = h / 2: n = 2 * n

Loop Until n 2 * m

If n 2 * m Then

MsgBox "计算次数预定太小，不能达到误差要求"

End If

tixingjffun = t2

End Function

'5.2.2 simpsonjffun 变步长Simpson积分法 -已测试

Private Function simpsonjffun(a As Single, b As Single, eps As Double, m As Long) As Double 'a、b分别为积分上下限，eps为误差，m为最大计算次数

Dim n As Long, i As Long

Dim h As Double, t1 As Double, t2 As Double, hh As Double, s1 As Double, s2 As Double

n = 1: h = b - a: t1 = h * (f(a) + f(b)) / 2

hh = h * (f((a + b) / 2)): s1 = (t1 + 2 * hh) / 3

Do

n = 2 * n: h = h / 2: t2 = (t1 + hh) / 2

t = 0

For i = 1 To n

t = t + f(a + (i - 0.5) * h)

Next i

hh = t * h

s2 = (t1 + 2 * hh) / 3

If Abs(s2 - s1) eps Then Exit Do

t1 = t2: s1 = s2

Loop Until n m

If n m Then MsgBox "计算次数预定太小，不能达到误差要求"

simpsonjffun = s2

End Function

'5.3 Rombergjffun Romberg积分法

Private Function rombergjffun(a As Single, b As Single, eps As Double) As Double

Dim k As Integer, n As Integer, h As Double

k = 0: n = 1: h = b - a

End Function

'5.5.1 ds1fun 求一阶导数 -已测试

Private Function ds1fun(x0 As Single, eps As Double) As Double 'x0为求导点，eps为误差

Dim h As Double, t1 As Double, t2 As Double

h = 1: t1 = (f(x0 + h) - f(x0 - h)) / (2 * h)

h = h / 2: t2 = (f(x0 + h) - f(x0 - h)) / (2 * h)

Do While Abs(t2 - t1) eps

t1 = t2

h = h / 2

t2 = (f(x0 + h) - f(x0 - h)) / (2 * h)

Loop

ds1fun = t2

End Function

'5.5.2 ds2fun 求二阶导数 -已测试

Private Function ds2fun(x0 As Single, eps As Double) As Double 'x0为求导点，eps为误差

Dim h As Double, t1 As Double, t2 As Double

h = 1: t1 = (f(x0 + h) + f(x0 - h) - 2 * f(x0)) / (h * h)

h = h / 2: t2 = (f(x0 + h) + f(x0 - h) - 2 * f(x0)) / (h * h)

Do While Abs(t2 - t1) eps

t1 = t2

h = h / 2

t2 = (f(x0 + h) + f(x0 - h) - 2 * f(x0)) / (h * h)

Loop

ds2fun = t2

End Function

拉格朗日插值的matlab代码

1、给出一列数据之后，作图如下：aa= randn(100,1);plot(aa);。

2、然后在做好的图中找到tools--basic fitting，打开如下对话框。

3、在打开的对话框中有多种数据插值方法，并可以给出插值的公式。使用cubic方法：于是可以看到插值后的曲线和插值公式。

4、一维插值相当于给出了xy的公式，比如我们上述命令中，aa的值为y，而aa中对应值的位置就是x。

5、还可以使用其他命令来进行数据插值。

6、matlab的interp1中还有nearest，next，previous，cubic等插值方法。

如何用matlab实现插值算法

实例展示

1

先看一个实例，最后再来说明一维插值在matlab中的用法。实例如下图，用13个节点作三种插值，并比较结果。

2

首先启动matlab，选择编辑器，再新建一个命令文件。

3

然后，在编辑器窗口中输入本题的代码。如下图所示。并保存，此处命名为yiwei。

4

最后再命令行窗口处输入yiwei，并敲入键盘上的enter建。最终得到的结果是插值与原来的13个数据点之间的比较图，可以看出结果很好。

END

命令解释

1

通过上面的例子，也知道了matlab进行一维插值的命令是interp1.

该命令的形式为y1=interp1(x0,y0,x1,'method').

功能：根据已知的数据（x0，y0），用method方法进行插值，然后计算x1对应的函数值y1.

2

其中的参数及其注意事项。

x0,y0是已知的数据向量，其中x应以升序或者降序排列，x1是插值点的自变量坐标向量；method是用来选择插值算法的，它可以取：‘linear’（线性插值）、‘cubic’（三次多项式插值）、‘nearst’（最近插值）、‘spline’（三次样条插值）。

牛顿插值法，用VB写代码？

Dim aa As Double, bb As Double '分别接收findway有根区间两端值的变量

Dim x(1) As Double '分别接收ercigenway的根

'1.0 ercigenway 求二次方程实根 -已测试

Private Sub ercigenway(a As Single, b As Single, c As Single) 'a、b、c对应为二次方程的系数

Dim d As Double

d = b ^ 2 - 4 * a * c

If d 0 Then

MsgBox "Δ小于0，没有实根", , "消息"

x(0) = 0: x(1) = 0

ElseIf d = 0 Then

x(0) = -b / (2 * a): x(1) = x(0)

Else

x(0) = (-b - Sgn(b) * Sqr(d)) / (2 * a): x(1) = c / (a * x(0))

End If

End Sub

'2.1 findway 等步长扫描有根区间 -已测试

Private Sub findway(ByVal a As Single, ByVal b As Single, h As Double) 'a、b分别为待扫描区间端点，h为步长

Dim a1 As Double

a1 = a

Do

If f(a1) * f(a1 + h) = 0 Then

aa = a1: bb = a1 + h

Exit Sub

End If

a1 = a1 + h

Loop While a1 b

If a1 b Then

MsgBox "没有找到有根区间，请换更小的步长试一下"

Exit Sub

End If

End Sub

'2.2 erfenfun 二分法求根 -已测试

Private Function erfenfun(ByVal a As Single, ByVal b As Single, eps As Double) 'a、b为有根区间端点，eps为误差

Dim x0 As Double, x1 As Double, x2 As Double, f0 As Double, f1 As Double, f2 As Double

x1 = a: x2 = b

Do

x0 = (x1 + x2) / 2

f0 = f(x0)

If f0 = 0 Then

Exit Do

Else

f1 = f(x1): f2 = f(x2)

If f0 * f1 0 Then

x2 = x0

Else

x1 = x0

End If

End If

Loop While Abs(x1 - x2) eps

x0 = (x1 + x2) / 2

erfenfun = x0

End Function

'2.4 newtonfxfun Newton切线法 -已测试

Private Function newtonfxfun(ByVal x0 As Double, eps As Double) As Double 'x0为附近根，eps为误差

Dim x1 As Double, f0 As Double, f1 As Double

x1 = x0

Do

x0 = x1

f0 = f(x0): f1 = fd(x0) 'fd表示f的导函数

If Abs(f1) eps Then

x1 = x0: Exit Do

End If

x1 = x0 - f0 / f1

Loop Until Abs(x1 - x0) eps

newtonfxfun = x1

End Function

'2.3 stediedaifun Seffensen加速迭代法 (方程形式为x-f(x)=0) -已测试

Private Function stediedaifun(ByVal x0 As Double, eps1 As Double, eps2 As Double) As Double 'x0为解析解附近的根，eps1为输出结果误差，eps2为迭代能否继续判断标准

Dim y As Double, z As Double, x1 As Double

x1 = x0

Do

x0 = x1

y = f(x0): z = f(y)

If Abs(z - 2 * y + x0) eps2 Then

MsgBox "为满足eps2条件，不能继续迭代"

Exit Function

End If

x1 = x0 - (y - x0) ^ 2 / (z - 2 * y + x0)

Loop Until Abs(x1 - x0) eps1

stediedaifun = x1

End Function

'2.5 newtonfxnfun n次代数方程Newton切线法 -已测试

Private Function newtonfxnfun(a() As Single, eps As Double, x0 As Double) As Double 'a()分别存储按降幂排列的方程的n个系数，eps为误差，x0为附近根

Dim k As Integer, n As Integer, f0 As Double, f1 As Double, x1 As Double

n = UBound(a)

x1 = x0

Do

x0 = x1

f0 = a(0): f1 = f0

For k = 1 To n - 1

f0 = a(k) + f0 * x0

f1 = f0 + f1 * x0

Next k

f0 = a(n) + f0 * x0

x1 = x0 - f0 / f1

Loop Until Abs(x1 - x0) eps

newtonfxnfun = x1

End Function

'2.6 linecutfun 弦截法 -已测试

Private Function linecutfun(ByVal x0 As Double, ByVal x1 As Double, eps As Double, n As Long) As Double 'n为迭代次数限制，x0、x1为有根区间端点，eps为误差

Dim f0 As Double, f1 As Double, f2 As Double

Dim x2 As Double, i As Long

f0 = f(x0): f1 = f(x1)

For i = 1 To n

x2 = x1 - (x1 - x0) * f1 / (f1 - f0)

f2 = f(x2)

If Abs(f2) eps Then

Exit For

End If

x0 = x1: x1 = x2: f0 = f1: f1 = f2

Next i

If i = n + 1 Then

MsgBox "要求的计算次数太低，没有达到精度要求"

End If

linecutfun = x2

End Function

'4.1 lagrangeczfun 拉格朗日插值法 -已测试

Private Function lagrangeczfun(a() As Double, ByVal u As Double) As Double 'a(1,n)存储n+1个节点，u为插值点

Dim i As Integer, j As Integer, n As Integer

Dim l As Double, v As Double

v = 0

n = UBound(a, 2)

For j = 0 To n

l = 1#

For i = 0 To n

If i = j Then GoTo hulue

l = l * (u - a(0, i)) / (a(0, j) - a(0, i))

hulue:

Next i

v = v + l * a(1, j)

Next j

lagrangeczfun = v

End Function

'4.2 newtonczfun newton插值法 -已测试

Private Function newtonczfun(a() As Double, u As Double) As Double 'a(1,n)存储n+1个节点，u为插值点

Dim n As Integer, i As Integer, j As Integer, k As Integer

Dim z() As Double, f() As Double, v As Double

n = UBound(a, 2)

ReDim z(n), f(n)

For i = 0 To n

z(i) = a(1, i)

Next i

For i = 1 To n

k = k + 1

For j = i To n

f(j) = (z(j) - z(j - 1)) / (a(0, j) - a(0, j - k))

Next j

For j = i To n

z(j) = f(j)

Next j

Next i

f(0) = a(1, 0)

v = 0

For i = n To 0 Step -1

v = v * (u - a(0, i)) + f(i)

Next i

newtonczfun = v

End Function

'4.3 hermiteczfun Hermite插值法 -已测试

Private Function hermiteczfun(a() As Double, fd() As Double, u As Double) As Double 'a(1,n)存储n+1个节点，fd(n)存储n+1个节点处导数值，u为插值点

Dim l() As Double, ld() As Double, g() As Double, h() As Double, aim As Double

Dim n As Integer, i As Integer, j As Integer

n = UBound(a)

ReDim l(n), ld(n), g(n), h(n)

aim = 0

For i = 0 To n

l(i) = 1: ld(i) = 0

For j = 0 To n

If j = i Then GoTo hulue

l(i) = l(i) * (u - a(0, j)) / (a(0, i) - a(0, j))

ld(i) = ld(i) + 1 / (a(0, i) - a(0, j))

hulue:

Next j

g(i) = (1 + 2 * (a(0, i) - u) * ld(i)) * l(i) * l(i)

h(i) = (u - a(0, i)) * l(i) * l(i)

aim = aim + g(i) * a(1, i) + h(i) * fd(i)

Next i

hermiteczfun = aim

End Function

'5.2.1 tixingjffun 变步长梯形积分法 -已测试

Private Function tixingjffun(a As Single, b As Single, eps As Double, m As Long) As Double 'a、b分别为积分上下限，eps为误差，m为最大计算次数

Dim h As Double, t1 As Double, t2 As Double, t As Double, hh As Double

Dim n As Long: n = 1

h = b - a: t1 = h * (f(a) + f(b)) / 2

Do

t = 0

For i = 1 To n

t = t + f(a + (i - 0.5) * h)

Next i

hh = h * t

t2 = (t1 + hh) / 2

If Abs(t2 - t1) eps Then Exit Do

t1 = t2: h = h / 2: n = 2 * n

Loop Until n 2 * m

If n 2 * m Then

MsgBox "计算次数预定太小，不能达到误差要求"

End If

tixingjffun = t2

End Function

'5.2.2 simpsonjffun 变步长Simpson积分法 -已测试

Private Function simpsonjffun(a As Single, b As Single, eps As Double, m As Long) As Double 'a、b分别为积分上下限，eps为误差，m为最大计算次数

Dim n As Long, i As Long

Dim h As Double, t1 As Double, t2 As Double, hh As Double, s1 As Double, s2 As Double

n = 1: h = b - a: t1 = h * (f(a) + f(b)) / 2

hh = h * (f((a + b) / 2)): s1 = (t1 + 2 * hh) / 3

Do

n = 2 * n: h = h / 2: t2 = (t1 + hh) / 2

t = 0

For i = 1 To n

t = t + f(a + (i - 0.5) * h)

Next i

hh = t * h

s2 = (t1 + 2 * hh) / 3

If Abs(s2 - s1) eps Then Exit Do

t1 = t2: s1 = s2

Loop Until n m

If n m Then MsgBox "计算次数预定太小，不能达到误差要求"

simpsonjffun = s2

End Function

'5.3 Rombergjffun Romberg积分法

Private Function rombergjffun(a As Single, b As Single, eps As Double) As Double

Dim k As Integer, n As Integer, h As Double

k = 0: n = 1: h = b - a

End Function

'5.5.1 ds1fun 求一阶导数 -已测试

Private Function ds1fun(x0 As Single, eps As Double) As Double 'x0为求导点，eps为误差

Dim h As Double, t1 As Double, t2 As Double

h = 1: t1 = (f(x0 + h) - f(x0 - h)) / (2 * h)

h = h / 2: t2 = (f(x0 + h) - f(x0 - h)) / (2 * h)

Do While Abs(t2 - t1) eps

t1 = t2

h = h / 2

t2 = (f(x0 + h) - f(x0 - h)) / (2 * h)

Loop

ds1fun = t2

End Function

'5.5.2 ds2fun 求二阶导数 -已测试

Private Function ds2fun(x0 As Single, eps As Double) As Double 'x0为求导点，eps为误差

Dim h As Double, t1 As Double, t2 As Double

h = 1: t1 = (f(x0 + h) + f(x0 - h) - 2 * f(x0)) / (h * h)

h = h / 2: t2 = (f(x0 + h) + f(x0 - h) - 2 * f(x0)) / (h * h)

Do While Abs(t2 - t1) eps

t1 = t2

h = h / 2

t2 = (f(x0 + h) + f(x0 - h) - 2 * f(x0)) / (h * h)

Loop

ds2fun = t2

End Function

c++，求插值。。高分求。。。答好再加！！

1.先将数组排序，得到沿坐标轴排列的(x,y)对

2.依次循环，作插值。插值方法可采用三点作抛物线，比如：要在1,2点之间作插值，就取1,2,3点的(x,y)数值，计算出通过1,2,3点的抛物线函数（实际就是解一个非常简单的三元一次方程），得到y=ax*x+bx+c 抛物线函数，利用该抛物线函数，带入要插值的x值（x1+x2)/2,得到y值，就产生了插值的新(x,y)点。

依次进行500次就ok了，最后一个点的抛物线可以选498,499,500三点来拟合。

知道原理后很简单，代码就不用写出来了吧。楼下如果有空，也可以帮忙把代码贴出来。

谁有拉格朗日插值法的python代码啊！急用啊！谢谢啦！

您好，#includestdio.h

#includestdlib.h

#includeiostream.h

typedef struct data

{

float x;

float y;

}Data;//变量x和函数值y的结构

Data d[20];//最多二十组数据

float f(int s,int t)//牛顿插值法，用以返回插商

{

if(t==s+1)

return (d[t].y-d[s].y)/(d[t].x-d[s].x);

else

return (f(s+1,t)-f(s,t-1))/(d[t].x-d[s].x);

}

float Newton(float x,int count)

{

int n;

while(1)

{

cout"请输入n值(即n次插值):";//获得插值次数

cinn;

if(n=count-1)// 插值次数不得大于count－1次

break;

else

system("cls");

}

//初始化t，y，yt。

float t=1.0;

float y=d[0].y;

float yt=0.0;

//计算y值

for(int j=1;j=n;j++)

{

t=(x-d[j-1].x)*t;

yt=f(0,j)*t;

//coutf(0,j)endl;

y=y+yt;

}

return y;

}

float lagrange(float x,int count)

{

float y=0.0;

for(int k=0;kcount;k++)//这儿默认为count－1次插值

{

float p=1.0;//初始化p

for(int j=0;jcount;j++)

{//计算p的值

if(k==j)continue;//判断是否为同一个数

p=p*(x-d[j].x)/(d[k].x-d[j].x);

}

y=y+p*d[k].y;//求和

}

return y;//返回y的值

}

void main()

{

float x,y;

int count;

while(1)

{

cout"请输入x[i],y[i]的组数，不得超过20组:";//要求用户输入数据组数

cincount;

if(count=20)

break;//检查输入的是否合法

system("cls");

}

//获得各组数据

for(int i=0;icount;i++)

{

cout"请输入第"i+1"组x的值:";

cind[i].x;

cout"请输入第"i+1"组y的值:";

cind[i].y;

system("cls");

}

cout"请输入x的值:";//获得变量x的值

cinx;

while(1)

{

int choice=3;

cout"请您选择使用哪种插值法计算："endl;

cout" (0):退出"endl;

cout" (1):Lagrange"endl;

cout" (2):Newton"endl;

cout"输入你的选择：";

cinchoice;//取得用户的选择项

if(choice==2)

{

cout"你选择了牛顿插值计算方法，其结果为：";

y=Newton(x,count);break;//调用相应的处理函数

}

if(choice==1)

{

cout"你选择了拉格朗日插值计算方法，其结果为：";

y=lagrange(x,count);break;//调用相应的处理函数

}

if(choice==0)

break;

system("cls");

cout"输入错误!!!!"endl;

}

coutx" , "yendl;//输出最终结果

}

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