A multidimensional generalization of some classes of free-derivative iterative methods to solve nonlinear equations
Tóm tắt
In this paper we extend to the multidimensional case six free-derivative iterative methods that are known in their scalar version. In order to construct new multidimensional iterative algorithms we develop a new idea based on two operators. All the schemes considered here are two-step methods in which the first step is Steffensen’s method and they have fourth-order local convergence, depending on the function. We analyze the efficiency of these six new algorithms and conclude which ones are the most efficient. We illustrate these results with some numerical examples, where their order of convergence is discussed. Finally, a study comparing the efficiency and elapsed time of the suggested methods supports the claimed theoretical results.
Tài liệu tham khảo
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