Fixed Point and Newton's Methods for Solving a Nonlinear Equation: From Linear to High-Order Convergence

DOI10.1137/130934799zbMath1305.65001OpenAlexW2095306051MaRDI QIDQ2937384

François Dubeau, Calvin Gnang

Publication date: 9 January 2015

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/130934799

zbMATH Keywords

Newton's methodnecessary conditionssufficient conditionsfixed point methodTaylor's expansionhigh-order methodSchröder's processes

Mathematics Subject Classification ID

Recurrences (11B37) Numerical computation of solutions to single equations (65H05) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis (65-01) Numerical approximation and computational geometry (primarily algorithms) (65D99) Acceleration of convergence in numerical analysis (65B99)

Related Items (5)

On the rediscovery of Halley's iterative method for computing the zero of an analytic function ⋮ Fixed point and Newton's methods in the complex plane ⋮ On the global convergence of Schröder's iterative formulae for real roots of algebraic equations ⋮ Asymptotic analysis and accurate approximate solutions for strongly nonlinear conservative symmetric oscillators ⋮ How Many Steps Still Left to $x$*?

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