On the global convergence of Schröder's iterative formulae for real roots of algebraic equations

DOI10.1016/j.cam.2018.05.041zbMath1398.65097OpenAlexW2805764141MaRDI QIDQ724512

Takemitsu Hasegawa, Sugiura, Hiroshi

Publication date: 26 July 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2018.05.041

zbMATH Keywords

nonlinear equationroot findingSchröder's methodglobal and monotonic convergencepolynomial real zeros

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05) Numerical computation of roots of polynomial equations (65H04)

Related Items (1)

On the global convergence of Schröder's iteration formula for real zeros of entire functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
• On the global convergence of Halley's iteration formula
• A family of root finding methods
• On Halley iteration
• Geometric constructions of iterative functions to solve nonlinear equations
• On extraneous fixed-points of the basic family of iteration functions
• A one parameter family of locally quartically convergent zero-finding methods
• On a high-order one-parameter family for the simultaneous determination of polynomial roots
• Padésche Näherungsbrüche und Iterationsverfahren höherer Ordnung
• A class of iterative methods for holomorphic functions
• On Schröder's families of root-finding methods
• Numerical Computing with IEEE Floating Point Arithmetic
• On the Julia set of König’s root–finding algorithms
• Numerical Algorithms Based on Analytic Function Values at Roots of Unity
• Fixed Point and Newton's Methods for Solving a Nonlinear Equation: From Linear to High-Order Convergence
• The Schwarzian-Newton method for solving nonlinear equations, with applications
• On an efficient method for the simultaneous approximation of polynomial multiple roots
• Generalizations of Laguerre’s Method: Higher Order Methods
• Root determination by use of Padé approximants
• Comments on a root finding method using Padé approximation
• Generalized Computation of Schröder Iteration Functions To Motivate Families of Julia and Mandelbrot-Like Sets
• The quasi-Laguerre iteration

This page was built for publication: On the global convergence of Schröder's iterative formulae for real roots of algebraic equations