Related papers: Computing tensor eigenvalues via homotopy methods
The theory of eigenvalues and eigenvectors is one of the fundamental and essential components in tensor analysis. Computing the dominant eigenpair of an essentially nonnegative tensor is an important topic in tensor computation because of…
In this paper, we propose a type of tensor-neural-network-based machine learning method to compute multi-eigenpairs of high dimensional eigenvalue problems without Monte-Carlo procedure. Solving multi-eigenvalues and their corresponding…
This paper studies tensor eigenvalue complementarity problems. Basic properties of standard and complementarity tensor eigenvalues are discussed. We formulate tensor eigenvalue complementarity problems as constrained polynomial…
In this paper we propose a homotopy method to compute the largest eigenvalue and a corresponding eigenvector of a nonnegative tensor. We prove that it converges to the desired eigenpair when the tensor is irreducible. We also implement the…
In this paper, we introduce a unified framework of Tensor Higher-Degree Eigenvalue Complementarity Problem (THDEiCP), which goes beyond the framework of the typical Quadratic Eigenvalue Complementarity Problem (QEiCP) for matrices. First,…
In this paper, the generalized eigenvalue complementarity problem for tensors (GEiCP-T) is addressed, which arises from the stability analysis of finite dimensional mechanical systems and find applications in differential dynamical systems.…
Several tensor eigenpair definitions have been put forth in the past decade, but these can all be unified under generalized tensor eigenpair framework, introduced by Chang, Pearson, and Zhang (2009). Given mth-order, n-dimensional…
In this paper, a homotopy continuation method for the computation of nonnegative Z-/H-eigenpairs of a nonnegative tensor is presented. We show that the homotopy continuation method is guaranteed to compute a nonnegative eigenpair.…
In this paper, we propose the tensor Noda iteration (NI) and its inexact version for solving the eigenvalue problem of a particular class of tensor pairs called generalized $\mathcal{M}$-tensor pairs. A generalized $\mathcal{M}$-tensor pair…
Let $A \in (\mathbb{C}^{n})^{\otimes p}$ be a complex tensor of order $p$. The pair $(v,\eta)\in\mathbb{C}^n\times \mathbb{C}$ is called an h-eigenpair of $A$, if $v\neq0$ and it satisfies $Av^{p-1}=\eta^{p-2} v$, where $Av^{p-1}$ is the…
The paper aims to propose a suitable method in finding the solution of tensor complementarity problem. The tensor complementarity problem is a subclass of nonlinear complementarity problems for which the involved function is defined by a…
Finding a Z-eigenpair of a symmetric tensor is equivalent to finding a KKT point of a sphere constrained minimization problem. Based on this equivalency, in this paper, we first propose a class of iterative methods to get a Z-eigenpair of a…
In this paper, we propose a novel tensor-based Dinkelbach--Type method for computing extremal tensor generalized eigenvalues. We show that the extremal tensor generalized eigenvalue can be reformulated as a critical subproblem of the…
In this paper, we consider the tensor generalized eigenvalue complementarity problem (TGEiCP), which is an interesting generalization of matrix eigenvalue complementarity problem (EiCP). First, we given an affirmative result showing that…
Let T be a general complex tensor of format $(n_1,...,n_d)$. When the fraction $\prod_in_i/[1+\sum_i(n_i-1)]$ is an integer, and a natural inequality (called balancedness) is satisfied, it is expected that T has finitely many minimal…
This work studies the problem of maximizing a higher degree real homogeneous multivariate polynomial over the unit sphere. This problem is equivalent to finding the leading eigenvalue of the associated symmetric tensor of higher order,…
Eigenvectors of tensors, as studied recently in numerical multilinear algebra, correspond to fixed points of self-maps of a projective space. We determine the number of eigenvectors and eigenvalues of a generic tensor, and we show that the…
Recent work on eigenvalues and eigenvectors for tensors of order m >= 3 has been motivated by applications in blind source separation, magnetic resonance imaging, molecular conformation, and more. In this paper, we consider methods for…
Real eigenpairs of symmetric tensors play an important role in multiple applications. In this paper we propose and analyze a fast iterative Newton-based method to compute real eigenpairs of symmetric tensors. We derive sufficient conditions…
Such problems as computation of spectra of spin chains and vibrational spectra of molecules can be written as high-dimensional eigenvalue problems, i.e., when the eigenvector can be naturally represented as a multidimensional tensor. Tensor…