An iterative method for the least squares solutions of the linear matrix equations with some constraint

Abstract

In this paper, an iterative method is presented to solve the following constrained minimum Frobenius norm residual problem:

where is a linear operator from R ^m×n onto , , is a linear self-conjugate involution operator. By this method, for any initial matrix , a solution can be obtained in finite iteration steps in the absence of roundoff errors. The least norm solution can be derived when an appropriate initial matrix is chosen. In addition, the optimal approximation solution in the solution set of the above problem to a given matrix can also be derived by this method. Several numerical examples are given to show the efficiency of the proposed iterative method.

Keywords:

• iterative method
• linear matrix equations system
• linear operator
• least norm solution
• optimal approximation solution

2000 AMS Subject Classifications :

• 15A24
• 65J10

Acknowledgements

This research work is granted financial support from Natural Science Foundation of Zhejiang Province (No.Y6090164), the University Natural Science Research Key Project of Anhui Province (No. KJ2010A253) and Natural Science Foundation of Huzhou (No. 2010YZ05).