Page 183 - Excel for Scientists and Engineers: Numerical Methods
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160 EXCEL: NUMERICAL METHODS
Figure 8-18 illustrates the three roots of the function obtained by using different
initial estimates.
Figure 8-18. Different starting values lead to different roots.
(folder 'Chapter 08 Examples', workbook 'Roots of Equations', worksheet 'Using Goal Seek')
The Secant Method
The secant method is similar to the Newton-Raphson method, except that it is
not necessary to calculate the slope of the curve. Instead, the slope is
approximated by using two values of x, as illustrated in Figure 8-19. Although
this may be a poor approximation to the tangent to the curve, it becomes more
and more accurate as the iterations approach the root. This method is not self-
starting, since values of the function at two adjacent x values must be provided to
begin the calculation. The calculations are illustrated in Figure 8-20, applied to
the function shown in equation 8-1.
I x2 X X1
Figure 8-19. The secant method for obtaining a root of a function.