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 Frechet derivative.
Third-order methods from quadrature formulae for solving systems of non-linear equations
FRONTINI, MARCO;
2004-01-01
Abstract
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 Frechet derivative.File in questo prodotto:
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