Finding the Largest Eigenvalue of a Nonnegative Tensor
Top Cited Papers
- 1 January 2010
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Matrix Analysis and Applications
- Vol. 31 (3), 1090-1099
- https://doi.org/10.1137/09074838x
Abstract
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.Keywords
This publication has 9 references indexed in Scilit:
- On eigenvalue problems of real symmetric tensorsJournal of Mathematical Analysis and Applications, 2009
- Perron-Frobenius theorem for nonnegative tensorsCommunications in Mathematical Sciences, 2008
- -eigenvalues of diffusion kurtosis tensorsJournal of Computational and Applied Mathematics, 2007
- Numerical multilinear algebra and its applicationsFrontiers of Mathematics in China, 2007
- Finding the spectral radius of a large sparse non-negative matrixANZIAM Journal, 2007
- Eigenvalues and invariants of tensorsJournal of Mathematical Analysis and Applications, 2006
- Eigenvalues of a real supersymmetric tensorJournal of Symbolic Computation, 2005
- A higher-order Markov model for the Newsboy's problemJournal of the Operational Research Society, 2003
- Einschließungssatz für die charakteristischen Zahlen von MatrizenMathematische Zeitschrift, 1942