Least squares solution of the quaternion Sylvester tensor equation

This paper is concerned with the solution to the least squares problem for the quaternion Sylvester tensor equation. An iterative algorithm based on tensor format is presented to solve this problem. The convergence properties of the proposed iterative method are studied. We also consider the best approximate problem related to quaternion Sylvester tensor equation. Numerical examples are provided to confirm the theoretical results, which demonstrate that the proposed algorithm is effective and feasible for solving the least squares problem of the quaternion Sylvester tensor equation.

Automated summary

This paper introduces an iterative algorithm based on tensor format to solve the least squares problem of the quaternion Sylvester tensor equation, and examines the convergence properties of this method. The best approximate problem related to the quaternion Sylvester tensor equation is also considered.