Order of Convergence of Regula Falsi Method is

An approximate solution to the equation f(x) = 0 on a finite interval [a, b] can be found using the Regula Falsi, often known as the method of false position. Here, f is a real-valued continuous function on [a, b] that meets the condition f(a) f(b) 0. Previous research demonstrated the convergence of this approach under the conditions that the first and second derivatives of the function f do not change the sign on the interval [a, b]. In this study, we do away with such presumptions and demonstrate the method's convergence for all continuous functions.

Answer - The order of convergence of Regula Falsi method is 1.618.

The Regula Falsi, also known as the method of false position or the false position method, is a very old and still-used approach to solving equations with a single unknown in mathematics. When we compare the power of the two sides, we have p=1+1/p, which results in p = 1 root(5). By ignoring the negative sign, we arrive at P = 1.618 as the Secant method's rate of convergence.

Summary: 

Order of Convergence of Regula Falsi Method is

The order of convergence of Regula Falsi method is 1.618. This is the oldest method for computing the real roots of an algebraic equation.

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