A Basis for Homogeneous Polynomial Solutions to Homogeneous Constant Coefficient PDE's: An Algorithmic Approach through Apolarity
ECOLE NORMALE SUPERIEURE PARIS (FRANCE) DEPT D'INFORMATIQUE
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Some recent methods of Computer Aided Geometric Design are related to the apolar bilinear form, an inner product on the space of homogeneous multivariate polynomials of a fixed degree, already known in 19th century invariant theory. A generalized version of this inner product was introduced in to derive in a straightforward way some of the recent results in CAGD. Here we extend this work by applying it to compute solution spaces of homogeneous constant coefficient PDEs.
- Numerical Mathematics
- Theoretical Mathematics