Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In 2011, Khattri and Abbasbandy developed an optimal two-step Jarratt-like method for approximating simple roots of a nonlinear equation.  develop their method for solving nonlinear systems of equations. The main feature of the extended methods is that it uses only one LU factorization which preserves and reduces computational complexities. Following this aim, the suggested method is generalized in such a way that  increase the order of convergence but  do not need new LU factorization. Convergence and complexity analysis are provided rigorously. Using some small and large systems, applicability along with some comparisons are illustrated.
['Saeid Abbasbandy', 'Parisa Bakhtiari', 'Alicia Cordero', 'Juan R. Torregrosa', 'Taher Lotfi']
I am writing a research paper on a idea New efficient methods for solving nonlinear systems of equations with arbitrary even order
[{"from": "human", "value": "I am writing a research paper on a idea New efficient methods for solving nonlinear systems of equations with arbitrary even order"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In 2011, Khattri and Abbasbandy developed an optimal two-step Jarratt-like method for approximating simple roots of a nonlinear equation.  develop their method for solving nonlinear systems of equations. The main feature of the extended methods is that it uses only one LU factorization which preserves and reduces computational complexities. Following this aim, the suggested method is generalized in such a way that  increase the order of convergence but  do not need new LU factorization. Convergence and complexity analysis are provided rigorously. Using some small and large systems, applicability along with some comparisons are illustrated."}]