Results on Newton methods. I: A unified approach for constructing perturbed Newton-like methods in Banach space and their applications

DOI10.1016/S0096-3003(98)10017-6zbMath0930.65063MaRDI QIDQ5906392

Ioannis K. Argyros

Publication date: 1 February 2000

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

zbMATH Keywords

Banach spaceradiative transfermajorant methodmonotone convergenceNewton-like methodsnonlinear operator equationsfast iterative methodsnonlinear integral equations of Uryson type

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) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07)

Related Items (1)

A mesh independence principle for inexact Newton-like methods and their discretizations under generalized Lipschitz conditions

Cites Work

• On the solution of equations with nondifferentiable and Ptak error estimates
• On the method of tangent hyperbolas in Banach spaces
• On a class of nonlinear integral equations arising in neutron transport
• A note on the Halley method in Banach spaces
• A special matrix equation and its application in microelectronics
• On an iterative algorithm of order 1.839… for solving nonlinear operator equations^∗)
• Quadratic equations and applications to Chandrasekhar's and related equations
• The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
• Convergence domains of certain iterative methods for solving nonlinear equations
• On the monotone convergence of general Newton-like methods
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