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We discuss a recursive family of iterative methods for the numerical approximation of roots of nonlinear functions in one variable. These methods are based on Newton-Cotes closed quadrature rules. We prove that when a quadrature rule with n + 1 nodes is used the resulting iterative method has convergence order at least n + 2, starting with the case n = 0… (More)

- Mário M. Graça
- 2008

A neutral fixed point of a real iteration map u becomes a super attracting fixed point using a suitable double newtonisation. The map u is so transformed into a map w which is here called the standard accelerator of u. The map w provides a unifying process to deal with a large set of fixed point sequences which are not convergent or converge slowly. Several… (More)

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