The symmetric solutions of the matrix inequality AX≥B in least-squares sense

Abstract

In this paper, we present an iterative method to compute the symmetric solutions of the matrix inequality AX≥B in least-squares sense. The presented iteration method can be also used to compute the symmetric solutions of the matrix equation AX=B and the consistent matrix inequality AX≥B. Numerical experiments are given to illustrate the usefulness of the proposed approach.

Keywords:

• iterative method
• matrix equation
• matrix inequality

Keywords:

• 2010 AMS Subject Classifications:
• 15A24
• 15A39
• 65F30

Acknowledgements

This research is supported by National Natural Science Foundation of China (11261014, 11101100) and Provincial Natural Science Foundation of Guangxi (0991238).