Editing Root-finding algorithm (section)

== Interpolation ==

Many root-finding processes work by [[interpolation]]. This consists in using the last computed approximate values of the root for approximating the function by a [[polynomial]] of low degree, which takes the same values at these approximate roots. Then the root of the polynomial is computed and used as a new approximate value of the root of the function, and the process is iterated.

Interpolating two values yields a line: a polynomial of degree one. This is the basis of the [[secant method]]. ''Regula falsi'' is also an interpolation method that interpolates two points at a time but it differs from the secant method by using two points that are not necessarily the last two computed points. Three values define a parabolic curve: a [[quadratic function]]. This is the basis of [[Muller's method]].