Journal of Global Optimization

, Volume 73, Issue 1, pp 193–221

# The least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint

• Baohua Huang
• Changfeng Ma
Article

## Abstract

In this paper, we present an iterative method for finding the least squares solution of a class of generalized Sylvester-transpose matrix equations with the norm inequality constraint. We prove that if the constrained matrix equations are consistent, the solution can be obtained within finite iterative steps in the absence of round-off errors; if constrained matrix equations are inconsistent, the least squares solution can be obtained within finite iterative steps in the absence of round-off errors. Finally, numerical examples are provided to illustrate the efficiency of the proposed method and testify the conclusions suggested in this paper.

## Keywords

Iterative method Generalized Sylvester-transpose matrix equations Norm inequality constraint Least squares solution Numerical experiments

## Notes

### Acknowledgements

The authors deeply thank the anonymous referees for helping to improve the original manuscript by valuable suggestions.

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