Convergence of the iteration of Halley's family and Smale operator class in Banach space

DOI10.1007/BF02901952zbMath0910.65036MaRDI QIDQ1267228

Xinghua Wang

Publication date: 15 December 1998

Published in: Science in China. Series A (Search for Journal in Brave)

zbMATH Keywords

convergenceHalley's methodNewton iterationerror estimateBanach spaceSmale operator

Mathematics Subject Classification ID

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

Related Items (6)

Uniform convergence of higher order quasi Hermite-Fejér interpolation ⋮ Two-square theorems for infinite matrices on certain fields ⋮ Convergence of the modified Halley's method for multiple zeros under Hölder continuous derivative ⋮ Local and global behavior for algorithms of solving equations ⋮ On the local convergence of a family of Euler-halley type iterations with a parameter ⋮ Convergence of iterations of Euler family under weak condition

Cites Work

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• On dominating sequence method in the point estimate and Smale's theorem
• Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
• Exponential polynomials
• On the efficiency of algorithms of analysis
• Convergence of Newton's method and uniqueness of the solution of equations in Banach space

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