A significant improvement on Newton's iterative method
type: Item
instance of: scholarly article
title: A significant improvement on Newton's iterative method
zbMATH Open document ID: 0940.65047
DOI: 10.1007/BF02452492
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 2000-07-10T00:00:00Z
review text: The author presents new ``Newton like'' methods for finding the zeros of a nonlinear and transcendental equation \(f(x)=0\), on the basis of Lyapunov's method of dynamic systems. The derived methods preserve quadratic convergence and the computational efficiency of Newton's method removing the monotonicity condition imposed on \(f(x): f'(x)\neq 0.\)
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 1383684
zbMATH Keywords: nonlinear equation
zbMATH Keywords: transcendental equation
zbMATH Keywords: Newton's method
zbMATH Keywords: Lyapunov's method
zbMATH Keywords: quadratic convergence
zbMATH Keywords: computational efficiency
zbMATH Keywords: monotonicity
author: Xinyuan Wu
reviewed by: Matthew He
MaRDI profile type: Publication
cites work: Q3961171
cites work: Q4067388
full work available at URL: https://doi.org/10.1007/bf02452492
OpenAlex ID: W2312423573
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description: scientific article; zbMATH DE number 1383684