Page 195 - Excel for Scientists and Engineers: Numerical Methods

172 EXCEL: NUMERICAL METHODS

Call EvaluateByBairstowMethod(N, A, Root)
Bairstow = Root()
End Function
..........................................................
Sub EvaluateByBairstowMethod(N, A, Root)
Code adapted from Shoup, "Numerical Methods for the Personal Computer".
Dim B() As Double, C() As Double
Dim M As Integer, I As Integer, J As Integer, IT As Integer
Dim P As Double, Q As Double, delP As Double, delQ As Double
Dim denom As Double, S1 As Double
Dim tolerance As Double
ReDirn B(N + 2), C(N + 2)
tolerance = 0.000000000000001
M=N
While M > 0
If M = 1 Then Root(M, 0) = -A(O): Call Sort(Root, N): Exit Sub
P = 0: Q = 0: delP = 1 : delQ = 1
For I = 0 To N: B(I) = 0: C(I) = 0: Next
For IT = 1 To 20
If Abs(delP) < tolerance And Abs(delQ) < tolerance Then Exit For
For J = 0 To M
B(M - J) =A(M - J) + P * B(M - J + 1) + Q * B(M- J + 2)
C(M - J) = B(M - J) + P * C(M - J + 1) + Q * C(M - J + 2)
Next J
denom = C(2) A 2 - C(l) * C(3)
delP = (-B(l) * C(2) + B(0) * C(3)) / denom
delQ = (-C(2) * B(0) + C(l) * B(1)) I denom
P = P + delP
Q = Q + delQ
Next IT
S1 =PA2+4*Q
If S1 i Then
0
'Handle imaginary roots
Root(M, 0) = P / 2: Root(M, 1) = Sqr(-S1) / 2
Root(M - 1, 0) = P I2: Root(M - 1, 1) = -Sqr(-S1) / 2
Else
'Handle real roots
Root(M, 0) = (P + Sqr(S1)) / 2
Root(M - 1, 0) = (P - Sqr(S1)) / 2
End If
For I = M To 0 Step -1: A(I) = B(I + 2): Next
M=M-2
Wend
End Sub
'+++++++++i+++++++++++i+++++i+++i~++++++++i+++i++++i+++i+++
Sub Sort(Root, N)
'SORT ROOTS IN ASCENDING ORDER
Dim I As Integer, J As Integer