1. Vector least-squares solutions for coupled singular matrix equations
- Author
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Kılıçman, Adem and Zhour, Zeyad Abdel Aziz Al
- Subjects
- *
MATRICES (Mathematics) , *ALGORITHMS , *NUMERICAL analysis , *ITERATIVE methods (Mathematics) - Abstract
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. [Copyright &y& Elsevier]
- Published
- 2007
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