High-order iterations for systems of nonlinear equations

In this paper, several families of order for the solution of systems of nonlinear equations are developed and compared to existing methods. The necessary and sufficient conditions for pth order of convergence are given in terms of parameter matrices and . Several choices of parameter matrix determining are suggested. The proposed families include some well-known methods as particular cases. The comparison is made based on the total cost of an iteration and the CPU time.

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