Halley's method for operators with unbounded second derivative

DOI10.1016/j.apnum.2006.05.001zbMath1252.65098OpenAlexW2066972720MaRDI QIDQ870309

N. E. Zubov

Publication date: 12 March 2007

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2006.05.001

zbMATH Keywords

nonlinear equations in Banach spacesHalley's methodsemilocal convergencenonlinear integral equationunbounded second derivative

Mathematics Subject Classification ID

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

Related Items (17)

On an efficient \(k\)-step iterative method for nonlinear equations ⋮ Third-order iterative methods with applications to Hammerstein equations: a unified approach ⋮ A variant of the Newton-Kantorovich theorem for nonlinear integral equations of mixed Hammerstein type ⋮ Derivative free algorithm for solving nonlinear equations ⋮ A semilocal convergence result for Newton's method under generalized conditions of Kantorovich ⋮ Convergence of the modified Halley's method for multiple zeros under Hölder continuous derivative ⋮ Extending the applicability of Newton's method for \(k\)-Fréchet differentiable operators in Banach spaces ⋮ Expanding the applicability of a third order Newton-type method free of bilinear operators ⋮ Newton-Kantorovich theorem for a family of modified Halley's method under Hölder continuity conditions in Banach space ⋮ Constructing third-order derivative-free iterative methods ⋮ Semilocal convergence of a sixth-order method in Banach spaces ⋮ Fourth-order iterations for solving Hammerstein integral equations ⋮ On a third-order Newton-type method free of bilinear operators ⋮ Majorizing sequences for Newton's method from initial value problems ⋮ The Theory of Kantorovich for Newton’s Method: Conditions on the Second Derivative ⋮ On the local convergence of a family of Euler-halley type iterations with a parameter ⋮ Extending the usage of Newton's method with applications to the solution of Bratu's equation

Cites Work

• On the method of tangent hyperbolas in Banach spaces
• On a convex acceleration of Newton's method
• Indices of convexity and concavity. Application to Halley method
• A note on the Halley method in Banach spaces
• Fewer convergence conditions for the Halley method
• Numerical Solvability of Hammerstein Integral Equations of Mixed Type
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Halley's method for operators with unbounded second derivative