Iterated function - Wikipedia
https://en.wikipedia.org/wiki/Iterated_functionThe notion f must be used with care when the equation g (x) = f(x) has multiple solutions, which is normally the case, as in Babbage's equationof the functional roots of the identity map. For example, for n = 2 and f(x) = 4x − 6, both g(x) = 6 − 2x and g(x) = 2x − 2 are solutions; so the expression f (x) doesn't denote a unique function, just as numbers have multiple algebraic roots. The issue is qu…
Iterative method - Wikipedia
https://en.wikipedia.org/wiki/Iterative_methodIf an equation can be put into the form f(x) = x, and a solution x is an attractive fixed point of the function f, then one may begin with a point x1 in the basin of attractionof x, and let xn+1 = f(xn) for n ≥ 1, and the sequence {xn}n ≥ 1 will converge to the solution x. Here xn is the nth approximation or iteration of x and xn+1 is the next or n + 1 iteration of x. Alternately, superscripts in parentheses are often used in numerical methods, so as not to interfere with subscripts with other meanings…