A unified approach for constructing fast two-step Newton-like methods

DOI10.1007/BF01292765zbMath0817.65042MaRDI QIDQ1345711

Ioannis K. Argyros

Publication date: 6 August 1995

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178670

zbMATH Keywords

error analysisnonlinear integral equationsBanach spaceradiative transfermajorant methodlinear operator equationfast two-step Newton-like methodsintegral equations of Uryson-typeNewton-Kantorovich-type hypotheses

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (10)

Improved error bounds for Newton-like iterations under Chen-Yamamoto conditions ⋮ An extension of the mesh independence principle for operator equations in Banach space ⋮ A mesh independence principle for inexact Newton-like methods and their discretizations under generalized Lipschitz conditions ⋮ A convergence analysis for directional two-step Newton methods ⋮ A study of convergence for a fourth-order two-point iteration in Banach spaces ⋮ A new semilocal convergence theorem for Newton's method in Banach space using hypotheses on the second Fréchet-derivative ⋮ On the convergence of inexact two-step Newton-like algorithms using recurrent functions ⋮ Convergence rates for inexact Newton-like methods at singular points and applications ⋮ Sufficient conditions for constructing methods faster than Newton's ⋮ Kantorovich's theorem on Newton's method in Riemannian manifolds

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