# 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 |
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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 |