scispace - formally typeset
Open AccessJournal ArticleDOI

A variant of Newton's method with accelerated third-order convergence

Sunethra Weerakoon, +1 more
- 01 Nov 2000 - 
- Vol. 13, Iss: 8, pp 87-93
Reads0
Chats0
TLDR
It is shown that the order of convergence of the new method is three, and computed results support this theory.
About: 
This article is published in Applied Mathematics Letters.The article was published on 2000-11-01 and is currently open access. It has received 813 citations till now. The article focuses on the topics: Steffensen's method & Secant method.

read more

Citations
More filters
Journal ArticleDOI

Gradient-based optimizer: A new metaheuristic optimization algorithm

Iman Ahmadianfar, +2 more
- 01 Nov 2020 - 
TL;DR: A novel metaheuristic optimization algorithm, gradient-based optimizer (GBO) is proposed, which yielded very promising results due to its enhanced capabilities of exploration, exploitation, convergence, and effective avoidance of local optima.
Journal ArticleDOI

Variants of Newton’s Method using fifth-order quadrature formulas☆

Alicia Cordero, +1 more
- 01 Jul 2007 - 
TL;DR: The third or fifth order of convergence of these variants of Newton's method for dimension one, and the second or third order in several variables, depending on the behaviour of the second derivative are proved.

Some variant of newtons method with third-order convergence

M. Frontini, +1 more
TL;DR: A general error analysis providing the higher order of convergence is given, and the best efficiency, in term of function evaluations, of two of this new methods is provided.
Journal ArticleDOI

Some variant of Newton's method with third-order convergence

M. Frontini, +1 more
- 10 Aug 2003 - 
TL;DR: In this article, a modification of the Newton's method is presented, which produces iterative methods with order of convergence three, and a general error analysis is given, and the best efficiency, in terms of function evaluations, of two of these methods is provided.
Journal ArticleDOI

Some new variants of Newton's method

Ahmet Yaşar Özban
- 01 Jun 2004 - 
TL;DR: Some new variants of Newton's method based on harmonic mean and midpoint integration rule have been developed and their convergence properties have been discussed and a comparison of the results and some of the existing ones are given.
References
More filters
Book

Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)

John E. Dennis, +1 more
TL;DR: In this paper, Schnabel proposed a modular system of algorithms for unconstrained minimization and nonlinear equations, based on Newton's method for solving one equation in one unknown convergence of sequences of real numbers.
Book

Numerical methods for unconstrained optimization and nonlinear equations

John E. Dennis, +1 more
TL;DR: Newton's Method for Nonlinear Equations and Unconstrained Minimization and methods for solving nonlinear least-squares problems with Special Structure.