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1. Linear convergence of an algorithm for computing the largest eigenvalue of a nonnegative tensor.

Author

Zhang, Liping and Qi, Liqun

Subjects
*STOCHASTIC convergence, *LINEAR systems, *ALGORITHMS, *EIGENVALUES, *TENSOR algebra, *ITERATIVE methods (Mathematics), *NUMERICAL analysis
Abstract

SUMMARY 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 & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Published
2012
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2. A practical two-term acceleration algorithm for linear systems.

Author

Wang, Chuan-Long and Meng, Guo-Yan

Subjects
*LINEAR systems, *ACCELERATION (Mechanics), *ALGORITHMS, *STOCHASTIC convergence, *INTERVAL analysis, *ITERATIVE methods (Mathematics), *CHEBYSHEV systems, *NUMERICAL analysis
Abstract

SUMMARY In this paper, a practical two-term acceleration algorithm is proposed, the interval of the parameter which guarantees the convergence of the acceleration algorithm is analyzed in detail. Further, the acceleration ratio of the new acceleration algorithm is obtained in advance. The new acceleration algorithm is less sensitive to the parameter than the Chebyshev semi-iterative method. Finally, some numerical examples show that the accelerated algorithm is effective. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Published
2012
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