Secant method

Summary

In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method. However, the secant method predates Newton's method by over 3000 years. The method For finding a zero of a function f, the secant method is defined by the recurrence relation. : x_n = x_{n-1} - f(x_{n-1}) \frac{x_{n-1} - x_{n-2}}{f(x_{n-1}) - f(x_{n-2})} = \frac{x_{n-2} f(x_{n-1}) - x_{n-1} f(x_{n-2})}{f(x_{n-1}) - f(x_{n-2})}. As can be seen from this formula, two initial values x0 and x1 are required. Ideally, they should be chosen close to the desired zero. Derivation of the method Starting with initial values x0 and x1, we construct a line through the points (x0, f(x0)) and (x1, f(x1)), as shown in the picture above. In slope–intercept form, the equation of this line is :

Official source

https://en.wikipedia.org/wiki/Secant_method

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