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2018-02-01

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cc-by-nc-nd (c) Elsevier, 2018
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/120580

The set of unattainable points for the Rational Hermite Interpolation Problem

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https://doi.org/10.1016/j.laa.2017.09.034

Abstract

We describe geometrically and algebraically the set of unattainable points for the Rational Hermite Interpolation Problem (i.e. those points where the problem does not have a solution). We show that this set is a union of equidimensional complete intersection varieties of odd codimension, the number of them being equal to the minimum between the degrees of the numerator and denominator of the problem. Each of these equidimensional varieties can be further decomposed as a union of as many rational (irreducible) varieties as input data points. We exhibit algorithms and equations defining all these objects.

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Geometria algebraica, Anells commutatius, Àlgebra commutativa

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Algebraic geometry, Commutative rings, Commutative algebra

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Articles publicats en revistes (Matemàtiques i Informàtica)

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CORTADELLAS BENÍTEZ, Teresa, D'ANDREA, Carlos and MONTORO LÓPEZ, M. Eulàlia. The set of unattainable points for the Rational Hermite Interpolation Problem. Linear Algebra and its Applications. 2018. Vol. 538, num. 116-142. ISSN 0024-3795. [consulted: 17 of June of 2026]. Available at: https://hdl.handle.net/2445/120580

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