多项式根与张量分解的本征求解器
Eigensolvers for polynomial roots and tensor decomposition
- Centre Inria at Université Côte d’Azur（蔚蓝海岸大学Inria中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出了用于求解多项式根与张量分解问题的符号-数值本征求解方法，通过交换算子联合特征向量实现相关计算，且在NAG4ALS包中完成了实现。
AI中文摘要：
计算特征值与特征向量是求解诸多非线性问题的核心。例如，求多项式方程组的根可归结为计算乘法算子的联合特征向量；张量分解则可通过张量的Catalecticant子矩阵的联合对角化实现。我们描述并阐释了符号-数值方法，该方法可通过计算交换算子的联合特征向量求解这些代数问题，分析其重数结构，还介绍了其在包NAG4ALS中的实现。
英文摘要：
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.
