The Unisolvence of Lagrange Interpolation with Symmetric Interpolation Space and Nodes in High Dimension
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911884623478784 |
|---|---|
| author | Xie, Yulin Tang, Yifa |
| author_facet | Xie, Yulin Tang, Yifa |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13430 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Unisolvence of Lagrange Interpolation with Symmetric Interpolation Space and Nodes in High Dimension Xie, Yulin Tang, Yifa Numerical Analysis 65D05 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. |
| title | The Unisolvence of Lagrange Interpolation with Symmetric Interpolation Space and Nodes in High Dimension |
| topic | Numerical Analysis 65D05 |
| url | https://arxiv.org/abs/2405.13430 |