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Recursively defined interpolation nodes for the simplex

Project description

recursivenodes: Recursive, parameter-free, explicitly defined interpolation nodes for simplices

This package includes one module level function, recursive_nodes(), which returns nodes for polynomial interpolation on the simplex in arbitrary dimensions.

The nodes have a few nice properties: they are explicitly constructed and fully symmetric, and their traces on edges are Lobatto-Gauss-Legendre nodes (or any other node set you wish to use). Among explicitly constructed nodes, they appear to have the best interpolation properties. You can find more details in the documentation, and even more in the preprint.

@misc{isaac2020recursive,
    title={Recursive, parameter-free, explicitly defined interpolation nodes for simplices},
    author={Tobin Isaac},
    year={2020},
    eprint={2002.09421},
    archivePrefix={arXiv},
    primaryClass={math.NA}
}

Requirements:

  • Only numpy is needed for recursive_nodes().
  • The lebesgue submodules requires scipy.
  • Testing requires coverage, pytest and matplotlib.
  • Building documentation additionally requires sphinx, sphinxcontrib-bibtex, and sphinxcontrib-tikz.

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