Vector least-squares solutions for coupled singular matrix equations

Authors:
Adem Kılıçman;Zeyad Abdel Aziz Al Zhour
Affiliations:
Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia (UPM), 43400, Serdang, Selangor, Malaysia;Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia (UPM), 43400, Serdang, Selangor, Malaysia
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 6
Cited 6

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Abstract

The weighted least-squares solutions of coupled singular matrix equations are too difficult to obtain by applying matrices decomposition. In this paper, a family of algorithms are applied to solve these problems based on the Kronecker structures. Subsequently, we construct a computationally efficient solutions of coupled restricted singular matrix equations. Furthermore, the need to compute the weighted Drazin and weighted Moore-Penrose inverses; and the use of Tian's work and Lev-Ari's results are due to appearance in the solutions of these problems. The several special cases of these problems are also considered which includes the well-known coupled Sylvester matrix equations. Finally, we recover the iterative methods to the weighted case in order to obtain the minimum D-norm G-vector least-squares solutions for the coupled Sylvester matrix equations and the results lead to the least-squares solutions and invertible solutions, as a special case.