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Line 8: 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>). The method can be summarized by the formula The method can be summarized by the formula <ref>{{Cite journal \| last1 = Ridders \| first1 = C. \| doi = 10.1109/TCS.1979.1084580 \| title = A new algorithm for computing a single root of a real continuous function \| journal = IEEE Transactions on Circuits and Systems \| volume = 26 \| pages = 979–980\| year = 1979 \| pmid = \| pmc = }}</ref> :<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>

Ridders' method: Difference between revisions