Third-order methods from quadrature formulae for solving systems of nonlinear equations. (English) Zbl 1050.65055

Authors’ summary: We extend to \(p\)-dimensional problems a modification of the Newton method, based on quadrature formulas of order at least one, which produces iterative methods with order of convergence three. A general error analysis providing the higher order of convergence is given. These new methods may be more efficient then other third-order methods as they do not require the use of the second-order Fréchet derivative.


65H10 Numerical computation of solutions to systems of equations
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