Ana C. Matos

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In this paper, after recalling the two definitions of the generalizations of the Padé approximants to orthogonal series, we will define the Padé–Legendre approximants of a Legendre series. We will propose two algorithms for the recursive computation of some sequences of these approximants. We will also estimate the speed of convergence of the columns of the(More)
In order to reduce the Gibbs phenomenon exhibited by the partial Fourier sums of a periodic function f , defined on [−π, π], discontinuous at 0, Driscoll and Fornberg considered so-called singular Fourier-Padé approximants constructed from the Hermite-Padé approximants of the system of functions (1, g1(z), g2(z)), where g1(z) = log(1 − z) and g2(z) is(More)
The aim of this paper is the study of the kernel and acceleration properties of sequence transformations of the form T n = L(S n =D n)=L(1=D n) , where (S n) is the sequence for which we want to compute the limit, (D n) is an error estimate and L is a linear diierence operator. We will obtain those properties for diierent classes of operators L and we will(More)
Currently the safe and responsible use of antibiotics is a world-wide concern as it promotes prevention of the increasing emergence of multiresistant bacterial strains. Considering that there is a noticeable decline of the available antibiotic pipeline able to combat emerging resistance in serious infection a major concern grows around the prosthetic joint(More)
For a recent new numerical method for computing so-called robust Padé approximants through SVD techniques, the authors gave numerical evidence that such approximants are insensitive to perturbations in the data, and do not have so-called spurious poles, that is, poles with a close-by zero or poles with small residuals. A black box procedure for eliminating(More)
In this paper we are going to study the convergence and acceleration properties of the vector E-algorithm when applied to some families of vector sequences of the form $$S_n - S = \sum\limits_{i = 0}^k {or} {\text{ }}S_n - S \sim \sum\limits_{i = 0}^\infty {a_i g_i (n)}$$ witha i ∈ ℂ,g i (n) ∈ ℂ p ∀i ⩾ 1. We will compare its properties with those of the(More)
The aim of this paper is to give some convergence results for some sequences of generalized Padé-type approximants. We will consider two types of interpolatory functionals: one corresponding to Langrange and Hermite interpolation and the other corresponding to orthogonal expansions. For these two cases we will give sufficient conditions on the generating(More)
In the Conjugate-Gradient-Squared method, a sequence of residualsr k defined byr k=P k 2 (A)r0 is computed. Coefficients of the polynomialsP k may be computed as a ratio of scalar products from the theory of formal orthogonal polynomials. When a scalar product in a denominator is zero or very affected by round-off errors, situations of breakdown or(More)