Root Finding by High Order Iterative Methods Based on Quadratures
Year: 2014
Type: preprint
Abstract: 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).
Source: arXiv (Cornell University)
Authors: Graça, Mario M., Lima, Pedro M.
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952073178