On the largest eigenvalue of a symmetric nonnegative tensor
نویسندگان
چکیده
منابع مشابه
On the largest eigenvalue of a symmetric nonnegative tensor
In this paper, some important spectral characterizations of symmetric nonnegative tensors are analyzed. In particular, it is shown that a symmetric nonnegative tensor has the following properties: (i) its spectral radius is zero if and only if it is a zero tensor; (ii) it is weakly irreducible (respectively, irreducible) if and only if it has a unique positive (respectively, nonnegative) eigenv...
متن کاملFinding the Largest Eigenvalue of a Nonnegative Tensor
In this paper we propose an iterative method for calculating the largest eigenvalue of an irreducible nonnegative tensor. This method is an extension of a method of Collatz (1942) for calculating the spectral radius of an irreducible nonnegative matrix. Numerical results show that our proposed method is promising. We also apply the method to studying higher-order Markov chains.
متن کاملLinear convergence of an algorithm for computing the largest eigenvalue of a nonnegative tensor
An iterative method for finding the largest eigenvalue of a nonnegative tensor was proposed by Ng, Qi, and Zhou in 2009. In this paper, we establish an explicit linear convergence rate of the Ng–Qi–Zhou method for essentially positive tensors. Numerical results are given to demonstrate linear convergence of the Ng–Qi–Zhou algorithm for essentially positive tensors. Copyright © 2011 John Wiley &...
متن کاملEfficient algorithms for computing the largest eigenvalue of a nonnegative tensor
Consider the problem of computing the largest eigenvalue for nonnegative tensors. In this paper, we establish the Q-linear convergence of a power type algorithm for this problem under a weak irreducibility condition. Moreover, we present a convergent algorithm for calculating the largest eigenvalue for any nonnegative tensors.
متن کاملA practical method for computing the largest M-eigenvalue of a fourth-order partially symmetric tensor
In this paper, we consider a quartic homogenous polynomial optimization problem over two unit spheres arising in nonlinear elastic material analysis and in entanglement studies in quantum physics. The problem is equivalent to computing the largest M-eigenvalue of a fourth-order tensor. To solve the problem, we propose a practical method whose validity is guaranteed theoretically. To make the se...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Numerical Linear Algebra with Applications
سال: 2013
ISSN: 1070-5325
DOI: 10.1002/nla.1885