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Gutiérrez, J. M.; Hernández, M. A.

A family of Chebyshev-Halley type methods in Banach spaces. (English) Zbl 0893.47043

Bull. Aust. Math. Soc. 55, No. 1, 113-130 (1997).
Summary: A family of third-order iterative processes (that includes Chebyshev and Halley’s methods) is studied in Banach spaces. Results on convergence and uniqueness of solutions are given, as well as error estimates. This study allows us to compare the most famous third-order iterative processes.

Cited in 4 Reviews
Cited in 149 Documents

MSC:

47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
65J15 Numerical solutions to equations with nonlinear operators

Keywords:

third-order iterative processes; convergence; uniqueness; error estimates
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\textit{J. M. Gutiérrez} and \textit{M. A. Hernández}, Bull. Aust. Math. Soc. 55, No. 1, 113--130 (1997; Zbl 0893.47043)
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