Page 234 - Excel for Scientists and Engineers: Numerical Methods

CHAPTER 9 SYSTEMS OF SIMULTANEOUS EQUATIONS 21 1

' Normalize pivot row
ForJ = 1 To N + 1
TempMatrix(K, J) = AugMatrix(K, J) / pivot
Next J
' Do the Gauss elimination.
For I = 1 To N
If I = K Then GoTo EndOfLoop2
For J = 1 To N + 1
TempMatrix(1, J) = AugMatrix(1, J) - AugMatrix(1, K) * TempMatrix(K, J)
Next J
EndOfLoop2: Next I
For I = 1 To N
ForJ = 1 To N + 1
AugMatrix(1, J) = TempMatrix(1, J)
Next J
Next I

Next K
End Sub
Figure 9-14. VBA code for the SimultEqnNL function procedure.
(folder 'Chapter 09 Simultaneous Equations', workbook 'NonLinNewton', module 'NewtonIterationlFunction')

As an example of the use of the SimultEqNL function, consider the following
set of four equations:
w3 + 2w2 + 3w + 4 = 12.828
wx + XY + YZ = -3.919
w2+2wx+x2= 1

w + x + y - z = -3.663
The corresponding Excel formulas were entered in Ell:E14 of Figure 9-15,
as follows:
=A1 1"3+2*A1 1 "2+3*A11+4

=A1 l*B11 +B1 I'CI 1 +C11 *D11
=A1 1 "2+2*A11 *B11 +B1 l"2

=A 1 1 +B 1 1 +C 1 1 -D 1 1
The constants were entered in cells F11 :F14 and trial values of the unknowns
in cells A1 1 :D11.