The Unisolvence of Lagrange Interpolation with Symmetric Interpolation Space and Nodes in High Dimension
<|reference_start|>The Unisolvence of Lagrange Interpolation with Symmetric Interpolation Space and Nodes in High Dimension: High-dimensional Lagrange interpolation plays a pivotal role in finite element methods, where ensuring the unisolvence and symmetry of its interpolation space and nodes set is crucial. In this paper, we leverage group action and group representation theories to precisely delineate the conditions for unisolvence. We establish a necessary condition for unisolvence: the symmetry of the interpolation nodes set is determined by the given interpolation space. Our findings not only contribute to a deeper theoretical understanding but also promise practical benefits by reducing the computational overhead associated with identifying appropriate interpolation nodes.<|reference_end|>
@article{xie2024the,
    title={The Unisolvence of Lagrange Interpolation with Symmetric Interpolation
  Space and Nodes in High Dimension},
    author={Yulin Xie, Yifa Tang},
    journal={arXiv preprint arXiv:2405.13430},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.13430},
    primaryClass={math.NA cs.NA}
}