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Analysis of semilocal convergence for ameliorated super-Halley methods with less computation for inversion
Published online by Cambridge University Press: 01 October 2016
Abstract
In this paper, the semilocal convergence for ameliorated super-Halley methods in Banach spaces is considered. Different from the results in [J. M. Gutiérrez and M. A. Hernández, Comput. Math. Appl. 36 (1998) 1–8], these ameliorated methods do not need to compute a second derivative, the computation for inversion is reduced and the $R$-order is also heightened. Under a weaker condition, an existence–uniqueness theorem for the solution is proved.
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- © The Author(s) 2016