Microsoft Office Tutorials and References
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Solving Recursive Equations
Solving Recursive Equations
A recursive equation is an equation in which a variable appears on both sides of the equal sign.
The following equations are examples of recursive equations:
x = 1/(x+1)
x = COS(x)
x = SQRT(X+5)
x = 2^(1/x)
x = 5 + (1/x)
You can solve a recursive equation by using an intentional circular reference.
This technique uses iterative calculations. By default, Excel doesn’t perform iterative
calculations, so you need to change a setting, by selecting the Enable Iterative
Calculation check box on the Formulas tab of the Excel Options dialog box (see
Figure 129-1).
Figure 129-1: To solve a recursive equation, you must specify the Enable Iterative Calculation option.
The first step is to convert the recursive equation into a self-referencing formula. To solve the
first equation, enter the following formula into cell A1:
The formula converges at 0.618033989, which is the value of x that satisfies the equation.
Excel uses an iterative process to calculate the solution. The maximum number of
iterations performed for each calculation is specified in Formulas tab of the Excel
Options dialog box. You might need to press F9 several times before the solution
stops changing.
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