that can \; be more relev ant to a mathematical model than the numerical acc uracy of the parameters. Beside its preservation\, symmetry shall also be exploited to alleviate the computational cost.

We revisit minimal d egree and least interpolation spaces [de Boor & \; Ron 1990] with symmetry adapted bases (rather t han the usual monomial bases). In these bases\, th e multivariate Vandermonde matrix \; (a.k.a co location matrix) is block diagonal as soon as the set of nodes is invariant. These blocks capture th e inherent redundancy in the computations. Further more any equivariance an interpolation problem mig ht have will be automatically preserved : the outp ut interpolant will have the same equivariance pro perty.

The special case of multivariate H ermite interpolation leads us to question the repr esentation of polynomial ideals. Grö\;bner bas es\, the preferred tool for algebraic computations \, breaks any kind of symmetry. The prior notion o f H-Bases\, introduced by Macaulay\, appears as mo re suitable.

Reference:

\; \ ;https ://dl.acm.org/citation.cfm?doid=3326229.3326247

\; \;https ://hal.inria.fr/hal-01994016 \; Joint work with \;Erick Rodriguez Bazan

LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR