Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle

By Feng Ding, Peter Xiaoping Liu, Jie Ding. Applied Mathematics and Computation, 2008

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The general coupled matrix equations over generalized bisymmetric matrices (2010, methodology): “The gradient-based iterative (GI) algorithms [15,20] and least squares based iterative algorithm [16] for solving (coupled) matrix equations are innovational and computationally efficient numerical algorithms and were presented based on the hierarchical identification principle [17,18] which regards”
On the generalized bisymmetric and skew-symmetric solutions of the system of generalized Sylvester matrix equations (2011, methodology): “The HGI algorithms [11,16] and HLSI algorithms [13,15,16] for solving general (coupled) matrix equations are innovative and computationally efficient numerical algorithms and were proposed based on the hierarchical identification principle [12,14] which regards the unknown matrix as the system param”
The generalized centro‐symmetric and least squares generalized centro‐symmetric solutions of the matrix equation AYB + CYTD = E (2011, methodology): “Ding and Chen introduced the hierarchical least squares-iterative (HLSI) algorithms for several coupled matrix equations [32, 33] and the hierarchical gradient-iterative (HGI) algorithms for general matrix equations [34, 35].”