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- Mário M. Graça
- Applied Mathematics and Computation
- 2009

- Mário M. Graça
- Experimental Mathematics
- 2002

- Mário M. Graça
- 2012

In order to approximate the integral I( f ) = ∫ b a f (x)dx, where f is a sufficiently smooth function, models for quadrature rules are developed using a given panel of n (n ≥ 2) equally spaced points. These models arise from the undetermined coefficients method, using a Newton’s basis for polynomials. Although part of the final product is algebraically… (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)

- MÁRIO M. GRAÇA
- 2002

- Mário M. Graça, Pedro Miguel Lima
- Applied Mathematics and Computation
- 2015

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)

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