VBA程序：二分法求方程的根.pdf
VBA程序：二分法求方程的根对于一般超越方程与高次代数方程求根的问题，可选用方法简单实用有效的不求导数的二分法，即在给定的寻根区间内，利用步步查找，二分缩小区间的方法，求出全部实根。二分法求根程序框图见后附件。主要标识符含义：A，B方程求根区间的左、右端点a,b H查根间距、跨步长度h EPS 计算精度值，0.00001 xA，yA变化过程中的左端点点值及函数值xB，YB变化过程中的右端点点值及函数值xC，yC变化过程中的中点点值及函数值算例已知方程式f(x)=x3-6x2+11x-6=0，求方程的根。给定条件x0.5,3.5，=0.00001，h=0.47。迭代求解后，可得到方程的三个实根：x1=1 x2=2 x3=3 VBA程序代码声明方程求解给定的条件Dim a As Double,b As Double,h As Double,eps As Double 声明数组,用来放置根Dim dblRoot()As Double 统计根的个数Dim lCount As Long Sub Main()Dim Xa As Double,Ya As Double,Xb As Double,Yb As Double 赋初值a=0.5 b=3.5 h=0.47 eps=0.00001 Xa=a Xb=a Ya=dblFx(Xa)Xb=Xb+h If Xb b Then Exit Sub Yb=dblFx(Xb)Call Root(Xa,Ya,Xb,Yb)End Sub Sub Root(Xa1 As Double,Ya1 As Double,Xb1 As Double,Yb1 As Double)If qqqRoot(Ya1,Yb1)Then Call qRoot(Xa1,Ya1,Xb1,Yb1)Else Xa1=Xb1 Ya1=Yb1 Xb1=Xb1+h If Xb1 b Then Exit Sub Yb1=dblFx(Xb1)符合求根条件则求根计算,否则继续调整求根区间If qqqRoot(Ya1,Yb1)Then Call qRoot(Xa1,Ya1,Xb1,Yb1)Else Call Root(Xa1,Ya1,Xb1,Yb1)End If End If End Sub 判断是否符合求根条件Function qqqRoot(dblYa2 As Double,dblYb2 As Double)As Boolean If dblYa2*dblYb2 eps And Abs(dblXa-dblXb)eps Then dblXc=(dblXa+dblXb)/2 dblYc=dblFx(dblXc)Call qqRoot(dblXa,dblYa,dblXb,dblYb,dblXc,dblYc)Else 求得一个根lCount=lCount+1 dblXd=(dblXa+dblXb)/2 将所求根保存在数组中ReDim Preserve dblRoot(1 To lCount)dblRoot(lCount)=dblXd 改变求根区间,以便获取下一个根dblXa=dblXb dblYa=dblYb dblXb=dblXb+h If dblXb b Then Exit Sub dblYb=dblFx(dblXb)Call Root(dblXa,dblYa,dblXb,dblYb)End If End Sub 判断并缩小求根区间Sub qqRoot(dblXa1 As Double,dblYa1 As Double,dblXb1 As Double,dblYb1 As Double,dblXc1 As Double,dblYc1 As Double)If dblYa1*dblYc1 0 Then dblXa1=dblXc1 dblYa1=dblYc1 Else dblXb1=dblXc1 dblYb1=dblYc1 End If Call qRoot(dblXa1,dblYa1,dblXb1,dblYb1)End Sub 要求根的方程式Function dblFx(dblX As Double)As Double dblFx=dblX*dblX*dblX-6*dblX*dblX+11*dblX-6 End Function 显示根Sub DisplayRoot()Dim i As Long Dim str As String lCount=0 调用求根程序Main 遍历并显示所求得的根For i=LBound(dblRoot)To UBound(dblRoot)str=str&方程的第&i&根是:&dblRoot(i)&Chr(10)Next i MsgBox str End Sub 参考资料：实用数值计算方法与程序附：二分法求方程的根框图送入 A,B,h,xAA xBB yAf(xA)xBxB+h xBB yBf(xB)yAyB00|yA-yB|或|xA-xB|0 xAxB yAyB 打印 xA,xB 开始结束T F T T T
