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CHAPTER 8 ROOTS OF EOUATIONS 153
Figure 8-8. A case with slow convergence of the Regula Falsi method.
(folder 'Chapter 08 Examples', workbook 'Roots of Equations', worksheet 'Regula Falsi (2)')
The Regu/a Falsi Method
with Correction for Slow Convergence
The preceding example shows that an unlucky choice of starting values can
lead to slow convergence. By examination of the example in Figure 8-7, it can
be seen that the ideal situation for rapid convergence occurs when, in almost
every cycle, there is a change in the value of both XI and x2, y1 and y2 or in the
sign of y1 or y2. Any one of these can be used to test for slow convergence.
The slow-convergence situation in Figure 8-8 was remedied by changing the
interpolation calculation so that if the value of x2 does not change from one cycle
to the next, the value of yz used in the interpolation is halved. The performance
of the modified formula is illustrated in Figure 8-9. The only change is the
formula in cell D4
=IF(C4=C3,D3/2,-1.04*LN(C4)-1.26*COS(C4)+0.0307*EXP(C4))
