TY - JOUR
T1 - Linear Convergence of the LZI Algorithm for Weakly Positive Tensors
AU - Liping Zhang, Liqun Qi & Yi Xu
JO - Journal of Computational Mathematics
VL - 1
SP - 24
EP - 33
PY - 2012
DA - 2012/02
SN - 30
DO - http://doi.org/10.4208/jcm.1110-m11si09
UR - https://global-sci.org/intro/article_detail/jcm/8414.html
KW - Irreducible nonnegative tensor, Weakly positive tensor, Largest eigenvalue,
Linear convergence.
AB - <p style="text-align: justify;">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.</p>