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

DOI10.1016/J.CAM.2019.02.035zbMATH Open1415.65112OpenAlexW2922079525MaRDI QIDQ2000615

Takemitsu Hasegawa, Sugiura, Hiroshi

Publication date: 28 June 2019

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.2019.02.035

zbMATH Keywords

entire functionnonlinear equationroot findingSchröder's methodglobal and monotonic convergence

Mathematics Subject Classification ID

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

Cites Work

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• On the global convergence of Schröder's iterative formulae for real roots of algebraic equations
• Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
• On the global convergence of Halley's iteration formula
• On extraneous fixed-points of the basic family of iteration functions
• A class of iterative methods for holomorphic functions
• On Schröder's families of root-finding methods
• On the Julia set of König’s root–finding algorithms
• Generalized Computation of Schröder Iteration Functions To Motivate Families of Julia and Mandelbrot-Like Sets
• Accuracy and Stability of Numerical Algorithms

Related Items (7)

Global convergence of the Durand-Kerner method applied to the equation \(z^ 3 = 0\) ⋮ A third-order iterative algorithm for inversion of cumulative central beta distribution ⋮ Regions of convergence and dynamics of Schröder-like iteration formulae as applied to complex polynomial equations with multiple roots ⋮ Unnamed Item ⋮ Disconnected Julia set of Halley's method for exponential maps ⋮ Computer tools for the construction and analysis of some efficient root-finding simultaneous methods ⋮ Analytical approximations to the Lambert \(W\) function

Uses Software

• mctoolbox

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