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LetˆL be a positive definite bilinear functional on the unit circle defined on P n , the space of polynomials of degree at most n. Then its Geronimus transformation L is defined byˆL(p, q) = L (z − α)p(z), (z − α)q(z) for all p, q ∈ P n , α ∈ C. GivenˆL, 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)

- Marc Van Barel, Matthias Humet, Laurent Sorber, Ku Leuven
- 2013

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)

- Matthias Humet, Marc Van Barel, Katholieke Universiteit Leuven, Marc, Van Barel
- 2011

Let L be a positive definite bilinear functional, then the Uvarov transformation of L is given by U(p, q) = L(p, q) + m p(α)q α −1 + m p α −1 q(α) where |α| > 1, m ∈ C. In this paper we analyze conditions on m for U to be positive definite in the linear space of polynomials of degree less than or equal to n. In particular, we show that m has to lie inside a… (More)

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