Eigensolvers for polynomial roots and tensor decomposition

2026-08-20

AI Summary

本文介绍了一种通过计算交换算子的联合特征向量来解决多项式根和张量分解问题的方法，并分析了其多重结构。

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.

Problem

• eigensolvers
• polynomial roots
• tensor decomposition
• joint eigenvectors

Innovation

• symbolic-numeric methods
• joint eigenvectors
• commuting operators
• tensor decomposition
• polynomial roots