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The false position method is one of the iterative methods of finding the roots of a non-linear equation of the form f(x) = 0. This method provides us with a better approximation of the roots of the equation.
The false position method tries to make the whole procedure more efficient by testing the sign of \(f\) at a point that is closer to the end of \(I_n\) where the magnitude of \(f\) is smaller. To be precise, we approximate \(y=f(x)\) by the equation of the straight line through \(\big(a_n,f(a_n)\big)\) and \(\big(b_n,f(b_n)\big)\text{.}\)
Regula Falsi Method, also known as the False Position Method, is a numerical technique used to find the roots of a non-linear equation of the form f(x)=.
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, in modified form, is still in use.
The poor convergence of the bisection method as well as its poor adaptability to higher dimensions (i.e., systems of two or more non-linear equations) motivate the use of better techniques. One such method is the Method of False Position.
Regula Falsi (also known as False Position Method) is one of bracketing and convergence guarenteed method for finding real root of non-linear equations. False Position Method is bracketing method which means it starts with two initial guesses say x0 and x1 such that x0 and x1 brackets the root i.e. f (x0)f (x1)< 0.
An algorithm for finding roots which retains that prior estimate for which the function value has opposite sign from the function value at the current best estimate of the root. In this way, the method of false position keeps the root bracketed (Press et al. 1992).