Volume 30, Issue 1
Linear Convergence of the LZI Algorithm for Weakly Positive Tensors

J. Comp. Math., 30 (2012), pp. 24-33

Published online: 2012-02

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• Abstract

We define weakly positive tensors and study the relations among essentially positive tensors, weakly positive tensors, and primitive tensors. In particular, an explicit linear convergence rate of the Liu-Zhou-Ibrahim(LZI) algorithm for finding the largest eigenvalue of an irreducible nonnegative tensor, is established for weakly positive tensors. Numerical results are given to demonstrate linear convergence of the LZI algorithm for weakly positive tensors.

• Keywords

Irreducible nonnegative tensor Weakly positive tensor Largest eigenvalue Linear convergence

74B99 15A18 15A69.