quadratic convergence

A sequence $\{x_i\}$ in a metric space $(X,d)$ is said to converge quadratically to $x^{*}$ if there is a constant $1>c>0$ such that $d(x_{i+1},x^{*})\le cd{(x_i,x^{*})}^2$ for all $i$.

The convergence is said to be of order $p$ if $d(x_{i+1},x^{*})\le cd{(x_i,x^{*})}^p$ for all $i$.

Title	quadratic convergence
Canonical name	QuadraticConvergence
Date of creation	2013-03-22 14:20:59
Last modified on	2013-03-22 14:20:59
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	8
Author	Koro (127)
Entry type	Definition
Classification	msc 41A25
Related topic	LinearConvergence