Linear convergence
= Linear convergence
{title2=$|e_{k+1}|/|e_k|\to\rho\in(0,1)$}
An <iteration of a map> has linear convergence to its <limit> when its nonzero errors $e_k=x_k-\alpha$ satisfy $|e_{k+1}|/|e_k|\to\rho$ for some $0<\rho<1$. The error eventually shrinks by approximately the same factor at each step. This is exact <order of convergence> one, in contrast to <quadratic convergence>.