New third-order method for solving systems of nonlinear equations. (English) Zbl 1163.65027

Summary: We present a new iterative method to solve systems of nonlinear equations. The main advantages of the method are: it has order three, it does not require the evaluation of any second or higher order Fréchet derivative and it permits that the Jacobian be singular at some points. Thus, the problem due to the fact that the Jacobian is numerically singular is solved. The third order convergence in both one dimension and for the multivariate case are given. The numerical results illustrate the efficiency of the method for systems of nonlinear equations.


65H10 Numerical computation of solutions to systems of equations
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