Trivariate polynomial approximation on Lissajous curves

Understand

We study Lissajous curves in the 3-cube, that generate algebraic cubature formulas on a special family of rank-1 Chebyshev lattices.

• These formulas are used to construct trivariate hyperinterpolation polynomials via a single 1-d Fast Chebyshev Transform (by the Chebfun package), and to compute discrete extremal sets of Fekete and Leja type for trivariate polynomial interpolation.
• Applications could arise in the framework of Lissajous sampling for MPI (Magnetic Particle Imaging).