Convergence analysis for a deformed Newton's method with third-order in Banach space under γ-condition

DOI10.1080/00207160701599683zbMath1169.65050OpenAlexW2097085160MaRDI QIDQ3615548

Yueqing Zhao, Qing-Biao Wu

Publication date: 20 March 2009

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160701599683

zbMATH Keywords

numerical exampleserror estimationBanach spacenonlinear operator equationthird-order convergence\(\gamma\)-conditionNewton-Kantorovich theorem deformed Newton's method

Mathematics Subject Classification ID

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

Related Items (7)

Newton-Kantorovich convergence theorem of a modified Newton's method under the gamma-condition in a Banach space ⋮ Larger convergence regions for an efficient two-step iterative method ⋮ Semilocal Convergence Theorem for a Newton-like Method ⋮ A Newton-type midpoint method with high efficiency index ⋮ Semilocal convergence analysis of \(S\)-iteration process of Newton-Kantorovich like in Banach spaces ⋮ Newton-Kantorovich and Smale uniform type convergence theorem for a deformed Newton method in Banach spaces ⋮ Convergence analysis for the King-Werner method under \(\gamma\)-conditions

Cites Work

• Unnamed Item
• A note on the Kantorovich theorem for Newton iteration
• A modification of Newton method with third-order convergence
• The midpoint method for solving nonlinear operator equations in Banach space
• Sufficient conditions for constructing methods faster than Newton's
• Convergence on the iteration of Halley family in weak conditions
• Convergence of Newton's method and uniqueness of the solution of equations in Banach spaces. II
• Modified Newton's method with third-order convergence and multiple roots
• A modified Newton method for rootfinding with cubic convergence.
• Some variant of Newton's method with third-order convergence.
• Third-order methods from quadrature formulae for solving systems of nonlinear equations.
• On the Newton-Kantorovich hypothesis for solving equations
• A modified Newton method with cubic convergence: the multivariate case
• Third-order convergence theorem by using majorizing function for a modified Newton method in Banach space
• On modified Newton methods with cubic convergence
• A variant of Newton's method with accelerated third-order convergence
• A modification of the classical Kantorovich conditions for Newton's method

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