Content deleted Content added
No edit summary |
No edit summary |
||
Line 7:
:<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_0,h(x_0))</math> and <math>(x_2,h(x_2))</math>, leading to a new value <math>x_3 </math>, between <math>x_0 </math> and <math>x_2 </math>,
:<math>x_3 = x_1 + (x_1 - x_0)\frac{\operatorname{sign}[f(x_0)]f(x_1)}{\sqrt{f(x_1)^2 - f(x_0)f(x_2)}},</math> 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''<sub>3</sub> if f(''x''<sub>3</sub>) has the opposite sign to f(''x''<sub>4</sub>), or otherwise whichever of ''x''<sub>1</sub> and ''x''<sub>2</sub> has f(x) of opposite sign to f(''x''<sub>4</sub>).
==References==
|