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Mathematical Problems in Engineering
Volume 2013, Article ID 819479, 7 pages
Research Article

A Gradient Based Iterative Solutions for Sylvester Tensor Equations

1School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China
2School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Received 27 December 2012; Accepted 13 February 2013

Academic Editor: Mohammad Younis

Copyright © 2013 Zhen Chen and Linzhang Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the numerical solution of the Sylvester tensor equation, which includes the Sylvester matrix equation as special case. By applying hierarchical identification principle proposed by Ding and Chen, 2005, and by using tensor arithmetic concepts, an iterative algorithm and its modification are established to solve the Sylvester tensor equation. Convergence analysis indicates that the iterative solutions always converge to the exact solution for arbitrary initial value. Finally, some examples are provided to show that the proposed algorithms are effective.