Vector least-squares solutions for coupled singular matrix equations |
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Authors: | Adem Kılıç man,Zeyad Abdel Aziz Al Zhour |
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Affiliation: | Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia (UPM), 43400, Serdang, Selangor, Malaysia |
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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. |
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Keywords: | 15A24 15A69 15A09 |
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