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In mathematics, the regula falsi, method of false position, or false position method is a very old method for solving an equation with one unknown; this method, ...
The false position method, also called the regula falsi method, is similar to the bisection method, but instead of using bisection search's middle of the interval it uses the x-intercept of the line that connects the plotted function values at the endpoints of the interval, that is
This means that the false position method always converges; however, only with a linear order of convergence. Bracketing with a super-linear order of convergence as the secant method can be attained with improvements to the false position method (see Regula falsi § Improvements in regula falsi) such as the ITP method or the Illinois method.
I concede that. But Regula Falsi and False Position are both popular and well-established names of the method. You'd be following established usage, and not leading, by using either one of those names. So that policy of sticking with established usage doesn't choose between the names "Regula Falsi" and "False Position".
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