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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.
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.
False position method: and Illinois method: 2-point, ... an iterative method to estimate parameters of a mathematical model from a set of observed data which ...
In numerical analysis, Ridders' method is a root-finding algorithm based on the false position method and the use of an exponential function to successively approximate a root of a continuous function (). The method is due to C. Ridders.
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Most numerical root-finding methods are iterative methods, producing a sequence of numbers that ideally converges towards a root as a limit. They require one or more initial guesses of the root as starting values, then each iteration of the algorithm produces a successively more accurate approximation to the root. Since the iteration must be ...
Limited-memory BFGS method — truncated, matrix-free variant of BFGS method suitable for large problems; Steffensen's method — uses divided differences instead of the derivative; Secant method — based on linear interpolation at last two iterates; False position method — secant method with ideas from the bisection method
The term "method of false position" has consistently been more common than "false position method" or "rule of false position" during the 20-21st centuries, according to Google ngrams. This article should be moved to Method of false position. Comments? --Macrakis 03:26, 19 July 2019 (UTC)