Editing Secant method (section)

{{Short description|Root-finding method}}{{Use American English|date = March 2019}}
[[Image:Secant method.svg|thumb|300px|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 [[Root of a function|roots]] of [[secant line]]s to better approximate a root of a [[Function (mathematics)|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 [[Regula falsi|method of false position]], which predates Newton's method by over 3000 years.<ref>{{Cite journal|last1=Papakonstantinou|first1=Joanna|last2=Tapia|first2=Richard|date=2013|title=Origin and evolution of the secant method in one dimension|url=https://www.jstor.org/stable/10.4169/amer.math.monthly.120.06.500|journal=American Mathematical Monthly|volume=120|issue=6|pages=500–518|doi=10.4169/amer.math.monthly.120.06.500|jstor=10.4169/amer.math.monthly.120.06.500 |s2cid=17645996 |url-access=subscription}}</ref>