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Symmetry Preserving Interpolation

Erick Rodriguez Bazan 1, 2 Evelyne Hubert 1, 2
1 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , NKUA | UoA - National and Kapodistrian University of Athens = University of Athens
Abstract : The article addresses multivariate interpolation in the presence ofsymmetry. Interpolation is a prime tool in algebraic computationwhile symmetry is a qualitative feature that can be more relevantto a mathematical model than the numerical accuracy of the pa-rameters. The article shows how to exactly preserve symmetryin multivariate interpolation while exploiting it to alleviate thecomputational cost. We revisit minimal degree and least interpo-lation with symmetry adapted bases, rather than monomial bases.This allows to construct bases of invariant interpolation spaces inblocks, capturing the inherent redundancy in the computations.We show that the so constructed symmetry adapted interpolationbases alleviate the computational cost of any interpolation problemand automatically preserve any aquivariance of thir interpolation problem might have.
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https://hal.archives-ouvertes.fr/hal-01994016
Contributor : Erick Dvid Rodriguez Bazan <>
Submitted on : Friday, January 25, 2019 - 11:26:52 AM
Last modification on : Tuesday, May 26, 2020 - 6:50:59 PM
Long-term archiving on: : Friday, April 26, 2019 - 1:09:00 PM

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Erick Rodriguez Bazan, Evelyne Hubert. Symmetry Preserving Interpolation. ISSAC 2019 - International Symposium on Symbolic and Algebraic Computation, Jul 2019, Beijing, China. ⟨10.1145/3326229.3326247⟩. ⟨hal-01994016⟩

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