Analysis of two Chebyshev-like third order methods free from second derivatives for solving systems of nonlinear equations

Some new efficient multipoint iterative methods for solving nonlinear systems of equations

“…Moreover, it is worth mentioning that although some of the scalar iteration can be extended, however, due to increasing in computational complexity, they have no practical interest. This matter has been discussed in [5,14,18] thoroughly and one can consult them.…”

“…Some other one point methods like Chebyshev and Halley [3,4] have been extended to their corresponding system versions with order of convergence three, but they use the first and second Frechet derivatives involved n 2 and n 3 function evaluations, respectively. On the other hand, it has been considerable attempts to derive methods free from second Frechet derivative having order of convergence three which most of them are not one step methods, and can be consulted in depth in [5]- [12] and references therein. There are few other mutipoint methods for approximating system solutions of nonlinear equations.…”

“…It is well known that, for x * + h ∈ R n lying in a neighborhood of a solution x * of the nonlinear system F (x) = 0, Taylor's expansion can be applied and we have 5) where…”

Increasing the order of convergence of iterative schemes for solving nonlinear systems

“…However, Babajee et al in [2] design Chebyshev-like schemes for solving nonlinear systems. In general, few papers for the multidimensional case introduce methods with high order of convergence.…”

Efficient high-order methods based on golden ratio for nonlinear systems

“…During the last years, numerous papers devoted to iterative methods for solving nonlinear systems have appeared in several journals. Some methods existing in the literature are based on the use of interpolation quadrature formulas (see [1][2][3][4]), or include the second partial derivative of the function F or different estimations of it (see [5][6][7][8]), or are Steffensen's type methods (see [9]), etc. We also pay attention to the known Jarratt's method (J) (see [10]) whose efficiency is widely recognized.…”