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Frontini, M.; Sormani, E.

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

Appl. Math. Comput. 149, No. 3, 771-782 (2004).
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.
Reviewer: B. Döring (Düsseldorf)

Cited in 103 Documents

MSC:

65H10 Numerical computation of solutions to systems of equations

Keywords:

third-order convergence; function evaluations; Newton method; quadrature formulas; error analysis
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\textit{M. Frontini} and \textit{E. Sormani}, Appl. Math. Comput. 149, No. 3, 771--782 (2004; Zbl 1050.65055)
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