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3D polynomial interpolation on general Lissajous-Chebyshev points
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README.md

LC3Ditp

3D polynomial interpolation on general Lissajous-Chebyshev nodes

                      

Version: 0.3 (01.10.2016)

Written by Peter Dencker and Wolfgang Erb

Description

The package LC3Ditp contains a Matlab implementation for trivariate polynomial interpolation on general Lissajous-Chebyshev points. This package syntesizes various interpolation schemes known in the literature.



The general description of the Lissajous-Chebyshev nodes and the polynomial interpolation is provided in the article [1].

  • To test the package use main_example.m

  • To plot the node points and the spectra use plot_LC3Dpts.m



   

As special cases it contains the following interpolation schemes:

  • Interpolation on the 3D Morrow-Patterson-Xu points for the frequency parameters (m,m,m) considered in [2].
  • Interpolation schemes based on single degenerate Lissajous curves for the frequency parameter (n,m,p), where n,m and p are relatively prime numbers [3].



   

Citation and Credits

The theory for this code was developed by Peter Dencker (Institute of Mathematics, University of Luebeck) and Wolfgang Erb (Department of Mathematics, University of Hawaii at Manoa). The general construction of the interpolation scheme is given in

  • [1]   Dencker, P. and Erb, W.
    A unifying theory for multivariate polynomial interpolation on general Lissajous-Chebyshev nodes
    arXiv:1711.00557v1 [math.NA] (2017)

Further references

  • [2]   Dencker, P. and Erb, W.
    Multivariate polynomial interpolation on Lissajous-Chebyshev nodes
    J. Approx. Theory 219 (2017), 15-45

  • [3]   De Marchi, S., Vianello, M. and Xu, Y.
    New cubature formulae and hyperinterpolation in three variables
    BIT 49 (1) (2009), 55–73.

The file plotregion.m was written by Per Bergström 2006-01-16. In this package it is used as an auxiliary program in plot_LC3Dpts.m to plot the polyhedral boundary of the spectral index sets.

License

Copyright (C) 2016 Peter Dencker, Wolfgang Erb

This software was written by Peter Dencker and Wolfgang Erb and developed at the University of Luebeck and the University of Hawaii

LC3Ditp is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.

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