Matthias Humet

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Let L̂ be a positive definite bilinear functional on the unit circle defined on Pn, the space of polynomials of degree at most n. Then its Geronimus transformation L is defined by L̂(p, q) = L ( (z − α)p(z), (z − α)q(z) ) for all p, q ∈ Pn, α ∈ C. Given L̂, there are infinitely many such L which can be described by a complex free parameter. The Hessenberg(More)
Let $\cal{L}$ be a positive definite bilinear functional, then the Uvarov transformation of $\cal{L}$ is given by $\,\mathcal{U}(p,q) = \mathcal{L}(p,q) + m\,p(\alpha)\overline{q}(\alpha^{-1}) + \overline{m}\,p(\overline{\alpha}^{-1})$ $\overline{q}(\overline{\alpha})$ where $|\alpha| > 1, m \in \mathbb{C}$ . In this paper we analyze conditions on m for(More)
Efficient and effective algorithms are designed to compute the coordinates of nearly optimal points for multivariate polynomial interpolation on a general geometry. “Nearly optimal” refers to the property that the set of points has a Lebesgue constant near to the minimal Lebesgue constant with respect to multivariate polynomial interpolation on a finite(More)
An algorithm is presented to compute good point sets and weights for discrete least squares polynomial approximation on a geometry Ω ⊂ R2. The criterion that is used is the minimisation of the Lebesgue constant of the corresponding least squares operator. In order to approximate the Lebesgue constant, we evaluate the Lebesgue function in a point set(More)
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