University of Cambridge > > Isaac Newton Institute Seminar Series > Symmetry Preserving Interpolation

Symmetry Preserving Interpolation

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact INI IT.

GCS - Geometry, compatibility and structure preservation in computational differential equations

In this talk I choose to present the PhD work of Erick Rodriguez Bazan. We address multivariate interpolation in the presence of symmetry as given by a finite group. 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. Beside its preservation, symmetry shall also be exploited to alleviate the computational cost.

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

The special case of multivariate Hermite interpolation leads us to question the representation of polynomial ideals. Gröbner bases, the preferred tool for algebraic computations, breaks any kind of symmetry. The prior notion of H-Bases, introduced by Macaulay, appears as more suitable.

Reference:   Joint work with  Erick Rodriguez Bazan

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2024, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity