Secant method

The first two iterations of the secant method. The red curve shows the function f, and the blue lines are the secants. For this particular case, the secant method will not converge to the visible root.

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, so it is considered a quasi-Newton method. Historically, it is as an evolution of the method of false position, which predates Newton's method by over 3000 years.[1]

  1. ^ Papakonstantinou, Joanna; Tapia, Richard (2013). "Origin and evolution of the secant method in one dimension". American Mathematical Monthly. 120 (6): 500–518. doi:10.4169/amer.math.monthly.120.06.500. JSTOR 10.4169/amer.math.monthly.120.06.500. S2CID 17645996 – via JSTOR.