A Chiseling Algorithm for Low-Rank Grassmann Decomposition of Skew-Symmetric Tensors
Abstract
A numerical algorithm to decompose an exact low-rank skew-symmetric tensor into a sum of elementary skew-symmetric tensors is introduced. The algorithm uncovers this Grassmann decomposition based on linear relations that are encoded by the kernel of the differential of the natural action of the general linear group on the tensor, following the ideas of Brooksbank et al. [ Detecting sparsity patterns in tensor data , arXiv:2408.17425v3, 2026]. The Grassmann decomposition can be recovered, up to scale, from the diagonalization of a generic element in this kernel. Numerical experiments illustrate that the algorithm is computationally efficient and quite accurate for mathematically low-rank tensors.
Fields of Study & Subjects
Tensor decomposition and applications
Elasticity and Material Modeling
Publication details
- Journal / source
- ACM Transactions on Mathematical Software
- Volume
- 52
- Issue
- 2
- Pages
- 1–35
- Publication date
- 12 May 2026
- Language
- EN