BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Symmetry Preserving Interpolation - Evelyne Hubert (INRIA Sophia A ntipolis\; INRIA Sophia Antipolis) DTSTART:20191126T140500Z DTEND:20191126T145000Z UID:TALK135274@talks.cam.ac.uk CONTACT:INI IT DESCRIPTION:In this talk I choose to present the PhD work of Erick R odriguez Bazan. We address multivariate interpolation in the presence of s ymmetry as given by a finite group. Interpolation is a prime tool in algeb raic computation while symmetry is a qualitative feature
that can \; be more relevant to a mathematical model than the numerical accuracy of the parameters. Beside its preservation\, symmetry shall also be exploite d to alleviate the computational cost.

We revisit minimal degree and least interpolation spaces [de Boor &\; Ron 1990] with symmetry ada pted bases (rather than the usual monomial bases). In these bases\, the mu ltivariate Vandermonde matrix \; (a.k.a colocation matrix) is block di agonal as soon as the set of nodes is invariant. These blocks capture the inherent redundancy in the computations. Furthermore any equivariance an i nterpolation problem might have will be automatically preserved : the outp ut interpolant will have the same equivariance property.

The spec ial case of multivariate Hermite interpolation leads us to question the re presentation of polynomial ideals. Grö\;bner bases\, the preferred too l for algebraic computations\, breaks any kind of symmetry. The prior noti on of H-Bases\, introduced by Macaulay\, appears as more suitable.

Reference:
\; \;https://dl.acm.org/cita tion.cfm?doid=3326229.3326247
\; \;https://hal.inria.fr/ hal-01994016 \; Joint work with \;Erick Rodriguez B azan

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