Page 188 - Excel for Scientists and Engineers: Numerical Methods

CHAPTER 8 ROOTS OF EOUATIONS 165

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Figure 8-25. Root of a function returned by the Newton-Raphson custom function.
(folder 'Chapter 08 Examples', workbook 'Newton-Raphson Function', sheet 'Newton-Raphson')
To use the custom function, enter the function in cell C7 by typing it
following the syntax above, or choose Insert-+Function.. ., choose the User
Defined category and choose the function from the list box. For the expression
argument, enter a reference to a cell containing the worksheet function (e.g., cell
87 in Figure 8-26). For the variable argument, enter A7, the cell reference of the
independent variable in the formula expression. If you do not enter a value for
the optional inifial_value argument, the value of the independent variable will be
used as the starting value. When you press ENTER, a root of the function is
returned, as shown in Figure 8-26.

Figure 8-26. Root of a function returned by the Newton-Raphson custom function.
(folder 'Chapter 08 Examples', workbook 'Newton-Raphson Function', sheet 'Newton-Raphson')
The root that is returned depends on the initial or trial value used by the
Newton-Raphson procedure. In this example, if a relatively large negative value
is used (e.g., -7), the root near -5 will be obtained. (See Figure 8-10 if this is not
clear.) Some caution must be exercised in choosing a trial value to direct the