PreprintarXiv licencearXiv
Eigensolvers for polynomial roots and tensor decomposition
Abstract
Computing eigenvalues and eigenvectors is at the heart of the solution of many non-linear problems. For instance, finding the roots of polynomial systems reduces to computing joint eigenvectors of operators of multiplication. Similarly, tensor decomposition can be performed via the joint diagonalization of submatrices of the Catalecticant of the tensor. We describe and illustrate symbolic-numeric methods for computing the solutions of these algebraic problems from the computation of joint eigenvectors of commuting operators, and for analysing their multiplicity structure, as well as their implementation in the package AlgebraicSolvers.jl.
Related
- Beyond Kruskal: Polynomial-Time Tensor Decomposition under the Lovitz-Petrov Condition
- Matrix roots of order n of a multivariate polynomial
- Improved computation of polynomial roots over number fields when using complex embeddings
- Affine Symmetries of Polynomial Roots with Multiplicities and Applications to Constacyclic Codes
- High-Order Predictor–Corrector Schemes for the Simultaneous Computation of Polynomial Roots with Known Multiplicities: Order Analysis and the Role of a Scalar-Derived Correction Factor
BibTeX
@misc{barrilli2026eigensolvers,
title = {{Eigensolvers for polynomial roots and tensor decomposition}},
author = {Enrica Barrilli and Bernard Mourrain},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.19818},
eprint = {2608.19818},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.19818},
}
RIS
TY - UNPB
TI - Eigensolvers for polynomial roots and tensor decomposition
AU - Enrica Barrilli
AU - Bernard Mourrain
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2608.19818
UR - https://arxiv.org/abs/2608.19818
AB - Computing eigenvalues and eigenvectors is at the heart of the solution of many non-linear problems. For instance, finding the roots of polynomial systems reduces to computing joint eigenvectors of operators of multiplication. Similarly, tensor decomposition can be performed via the joint diagonalization of submatrices of the Catalecticant of the tensor. We describe and illustrate symbolic-numeric methods for computing the solutions of these algebraic problems from the computation of joint eigenvectors of commuting operators, and for analysing their multiplicity structure, as well as their implementation in the package AlgebraicSolvers.jl.
ER -