In this paper, the Galerkin projection method is used for solving the semi Sylvester equation. Firstly the semi Sylvester equation is reduced to the multiple linear systems. To apply the Galerkin projection method, so...In this paper, the Galerkin projection method is used for solving the semi Sylvester equation. Firstly the semi Sylvester equation is reduced to the multiple linear systems. To apply the Galerkin projection method, some propositions are presented. The presented scheme is compared with the L-GL-LSQR algorithm in point of view CPU-time and iteration number. Finally, some numerical experiments are presented to show that the efficiency of the new scheme.展开更多
In this paper, a new iterative solution method is proposed for solving multiple linear systems A(i)x(i)=b(i), for 1≤ i ≤ s, where the coefficient matrices A(i) and the right-hand sides b(i) are arbitrary in general....In this paper, a new iterative solution method is proposed for solving multiple linear systems A(i)x(i)=b(i), for 1≤ i ≤ s, where the coefficient matrices A(i) and the right-hand sides b(i) are arbitrary in general. The proposed method is based on the global least squares (GL-LSQR) method. A linear operator is defined to connect all the linear systems together. To approximate all numerical solutions of the multiple linear systems simultaneously, the GL-LSQR method is applied for the operator and the approximate solutions are obtained recursively. The presented method is compared with the well-known LSQR method. Finally, numerical experiments on test matrices are presented to show the efficiency of the new method.展开更多
文摘In this paper, the Galerkin projection method is used for solving the semi Sylvester equation. Firstly the semi Sylvester equation is reduced to the multiple linear systems. To apply the Galerkin projection method, some propositions are presented. The presented scheme is compared with the L-GL-LSQR algorithm in point of view CPU-time and iteration number. Finally, some numerical experiments are presented to show that the efficiency of the new scheme.
文摘In this paper, a new iterative solution method is proposed for solving multiple linear systems A(i)x(i)=b(i), for 1≤ i ≤ s, where the coefficient matrices A(i) and the right-hand sides b(i) are arbitrary in general. The proposed method is based on the global least squares (GL-LSQR) method. A linear operator is defined to connect all the linear systems together. To approximate all numerical solutions of the multiple linear systems simultaneously, the GL-LSQR method is applied for the operator and the approximate solutions are obtained recursively. The presented method is compared with the well-known LSQR method. Finally, numerical experiments on test matrices are presented to show the efficiency of the new method.
