Multivariate interpolation: Preserving and exploiting symmetry

Interpolation is a prime tool in algebraic computation while symmetry qualitative feature that can be more relevant to mathematical model than the numerical accuracy of parameters. The article shows how exactly preserve multivariate interpolation exploiting it alleviate computational cost. We revisit minimal degree and least with adapted bases, rather monomial bases. For space linear forms invariant under group action, we construct bases spaces blocks, capturing inherent redundancy computations. With so constructed uniquely defined interpolant automatically preserves any equivariance problem might have. Even no equivariance, cost obtain alleviated thanks smaller size matrices inverted.