Trivariate polynomial approximation on Lissajous curves ∗

  title={Trivariate polynomial approximation on Lissajous curves ∗},
  author={Len Bos and Stefano De Marchi and Marco Vianello},
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). 2010 AMS subject… CONTINUE READING


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