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The method of false position provides an exact solution for linear functions, but more direct algebraic techniques have supplanted its use for these functions. However, in numerical analysis, double false position became a root-finding algorithm used in iterative numerical approximation techniques.
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
Illustration of the false positition method. Created by Jitse Niesen using Xfig. Date: 19 June 2006 (original upload date) Source: No machine-readable source provided. Own work assumed (based on copyright claims). Author: No machine-readable author provided. Jitse Niesen assumed (based on copyright claims). SVG development
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.
The problems cover elementary arithmetic; fractions; inverse proportion; factorization of numbers; geometric progressions, in particular interest rate calculations and handling of errors; conversion between different units; the false position method for finding roots and the extraction of approximate square roots; calculation of the volume of ...
We are in a false position, we have great players and today it all clicked. "We knew they would come out [in the second half] and it would be hard. Luckily I helped the team today.
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