Semilocal convergence of a class of modified super-Halley methods in Banach spaces

DOI10.1007/s10957-012-9985-9zbMath1250.65075OpenAlexW2036522182MaRDI QIDQ438773

Xiuhua Wang, Jisheng Kou, Chuanqing Gu

Publication date: 31 July 2012

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10957-012-9985-9

zbMATH Keywords

iterative methodnonlinear equations in Banach spacessemilocal convergencerecurrence relationssuper-Halley method

Mathematics Subject Classification ID

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

Related Items (8)

Local convergence for a family of iterative methods based on decomposition techniques ⋮ The convergence theorem for fourth-order super-Halley method in weaker conditions ⋮ Third-order Newton-type methods combined with vector extrapolation for solving nonlinear systems ⋮ Recurrence relations for a family of iterations assuming Hölder continuous second order Fréchet derivative ⋮ Convergence analysis for a family of improved super-Halley methods under general convergence condition ⋮ Ball convergence for second derivative free methods in Banach space ⋮ Extended domain for fifth convergence order schemes ⋮ On the semi-local convergence analysis of higher order iterative method in two folds

Cites Work

• Semilocal convergence of a sixth-order Jarratt method in Banach spaces
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• A variant of super-Halley method with accelerated fourth-order convergence
• Recurrence relations for rational cubic methods. I: The Halley method
• Recurrence relations for the super-Halley method
• A parallel, implicit, cell-centered method for two-phase flow with a preconditioned Newton-Krylov solver
• Recurrence relations for Chebyshev-type methods
• Recurrence relations for a Newton-like method in Banach spaces
• A family of modified super-Halley methods with fourth-order convergence
• New iterations of \(R\)-order four with reduced computational cost
• Semilocal convergence of a multipoint fourth-order super-Halley method in Banach spaces
• SEMILOCAL CONVERGENCE OF A STIRLING-LIKE METHOD IN BANACH SPACES
• An acceleration of Newton's method: Super-Halley method
• Chebyshev's approximation algorithms and applications

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