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 theframework of Lissajous sampling for MPI (Magnetic Particle Imaging).
Trivariate polynomial approximation on Lissajous curves
BOS, LEONARD PETER;DE MARCHI, STEFANO;VIANELLO, MARCO
2017
Abstract
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 theframework of Lissajous sampling for MPI (Magnetic Particle Imaging).File in questo prodotto:
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