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Higher order Jarratt-like iterations for solving systems of nonlinear equations. (English) Zbl 1508.65054

Summary: In this article, we propose a new family of methods, such as Jarratt, with the fifth and sixth order. This includes some popular methods as special cases. We propose four different selection for parameter matrix \(T_k\). The main advantage of the proposed methods is that they work well for any value of parameter “\(a\)” in the first stage of iterations, while the existing methods work only for some \(a\) (\(2/3\) or \(1/2\)). Thus, we extend essentially the domain of applicability of the original ones. Based on the computational efficiency analysis, we also made a selection of some high-efficiency ones among the families.

MSC:

65H10 Numerical computation of solutions to systems of equations
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