Root Finding by High Order Iterative Methods Based on Quadratures

We discuss a recursive family of iterative methods for the numerical approximation of roots of nonlinear functions in one variable. These methods are based on Newton-Cotes closed quadrature rules. We prove that when a quadrature rule with \(n+1\) nodes is used the resulting iterative method has conv...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2014-09
Main Authors: Graça, Mario M, Lima, Pedro M
Format: Article
Language:English
Subjects:
Approximation
Iterative methods
Mathematical analysis
Newton methods
Numerical methods
Quadratures
Recursive methods
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We discuss a recursive family of iterative methods for the numerical approximation of roots of nonlinear functions in one variable. These methods are based on Newton-Cotes closed quadrature rules. We prove that when a quadrature rule with \(n+1\) nodes is used the resulting iterative method has convergence order at least \(n+2\), starting with the case \(n=0\) (which corresponds to the Newton's method).
ISSN:2331-8422