FINDING THE LARGEST EIGENVALUE OF A NONNEGATIVE TENSOR

FINDING 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 metho...

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Veröffentlicht in:SIAM journal on matrix analysis and applications 2009-01, Vol.31 (3), p.1090-1099
Hauptverfasser: NG, Michael, LIQUN QI, GUANGLU ZHOU
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Eigenvalues
Exact sciences and technology
Iterative methods
Linear and multilinear algebra, matrix theory
Markov analysis
Markov chains
Mathematical analysis
Mathematical models
Mathematics
Matrix
Nonlinear algebraic and transcendental equations
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Numerical methods in probability and statistics
Sciences and techniques of general use
Spectra
Studies
Tensors
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Zusammenfassung: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. [PUBLICATION ABSTRACT]
ISSN:0895-4798
1095-7162
DOI:10.1137/09074838X