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Multivariate Interpolation: Preserving and Exploiting Symmetry

Erick Rodriguez Bazan 1, 2 Evelyne Hubert 1, 2
1 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , NKUA - National and Kapodistrian University of Athens
Abstract : Interpolation is a prime tool in algebraic computation while symmetry is a qualitative feature that can be more relevant to a mathematical model than the numerical accuracy of the parameters. The article shows how to exactly preserve symmetry in multivariate interpolation while exploiting it to alleviate the computational cost. We revisit minimal degree and least interpolation with symmetry adapted bases, rather than monomial bases. For a space of linear forms invariant under a group action, we construct bases of invariant interpolation spaces in blocks, capturing the inherent redundancy in the computations. With the so constructed symmetry adapted interpolation bases, the uniquely defined interpolant automatically preserves any equivariance the interpolation problem might have. Even with no equivariance, the computational cost to obtain the interpolant is alleviated thanks to the smaller size of the matrices to be inverted.
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https://hal.inria.fr/hal-03123418
Contributor : Evelyne Hubert Connect in order to contact the contributor
Submitted on : Wednesday, January 27, 2021 - 7:36:10 PM
Last modification on : Thursday, January 20, 2022 - 4:13:15 PM
Long-term archiving on: : Wednesday, April 28, 2021 - 7:23:44 PM

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  • HAL Id : hal-03123418, version 1

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Erick Rodriguez Bazan, Evelyne Hubert. Multivariate Interpolation: Preserving and Exploiting Symmetry. Journal of Symbolic Computation, Elsevier, In press. ⟨hal-03123418⟩

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