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.
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