A new convergence theorem for the Jarratt method in Banach space

DOI10.1016/S0898-1221(98)00179-5zbMath0933.65064OpenAlexW2089330273MaRDI QIDQ1125040

Ioannis K. Argyros

Publication date: 30 March 2000

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0898-1221(98)00179-5

zbMATH Keywords

convergencenumerical exampleBanach spacenonlinear operator equationFréchet-derivativeJarratt methodNewton-Kantorovich hypothesis

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (12)

Newton-Kantorovich convergence theorem of a new modified Halley's method family in a Banach space ⋮ A new convergence theorem for the Jarratt method in Banach space ⋮ Weak convergence conditions for inexact Newton-type methods ⋮ On the semilocal convergence of efficient Chebyshev-secant-type methods ⋮ Unnamed Item ⋮ A weak Kantorovich existence theorem for the solution of nonlinear equations ⋮ A new semilocal convergence theorem for Newton's method in Banach space using hypotheses on the second Fréchet-derivative ⋮ A Newton-Kantorovich theorem for equations involving \(m\)-Fréchet differentiable operators and applications in radiative transfer ⋮ A Newton-Kantorovich convergence theorem for the inverse-free Jarratt method in Banach space ⋮ Enlarging the domain of starting points for Newton's method under center conditions on the first Fréchet-derivative ⋮ Extended domain for fifth convergence order schemes ⋮ New variants of Jarratt's method with sixth-order convergence

Cites Work

• A new semilocal convergence theorem for Newton's method
• A new convergence theorem for the Jarratt method in Banach space
• Some notions of nonstationary multistep iteration processes
• The Jarratt method in Banach space setting
• The application of an inverse-free Jarratt-type approximation to nonlinear integral equations of Hammerstein-type
• Some efficient fourth order multipoint methods for solving equations
• Some Fourth Order Multipoint Iterative Methods for Solving Equations
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