Ridders' method: Difference between revisions

Revision as of 11:42, 31 May 2017

Revision as of 11:43, 31 May 2017

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:<math>e^{a(x_1 - x_0)} = \frac{f(x_1)+\operatorname{sign}[f(x_2)]\sqrt{f(x_1)^2 - f(x_0)f(x_2)}}{f(x_2)} .</math>

The false position method is then applied to the points <math>(x_1x_0,h(x_1x_0))</math> and <math>(x_0x_2,h(x_0x_2))</math>, leading to a new value ''x''<submath>3x_3 </submath>, between ''x''<submath>0x_0 </submath> and ''x''<submath>2x_2 </submath>, which can be used as one of the two bracketing values in the next step of the iteration.

The other bracketing value is taken to be ''x''₃ if f(''x''₃) has the opposite sign to f(''x''₄), or otherwise whichever of ''x''₁ and ''x''₂ has f(x) of opposite sign to f(''x''₄).