For the linear least squares problem with coefficient matrix columns being highly correlated, we develop a greedy randomized Gauss-Seidel method with oblique direction. Then the corresponding convergence result is ded...For the linear least squares problem with coefficient matrix columns being highly correlated, we develop a greedy randomized Gauss-Seidel method with oblique direction. Then the corresponding convergence result is deduced. Numerical examples demonstrate that our proposed method is superior to the greedy randomized Gauss-Seidel method and the randomized Gauss-Seidel method with oblique direction.展开更多
The preconditioned Gauss-Seidel type iterative method for solving linear systems, with the proper choice of the preconditioner, is presented. Convergence of the preconditioned method applied to Z-matrices is discussed...The preconditioned Gauss-Seidel type iterative method for solving linear systems, with the proper choice of the preconditioner, is presented. Convergence of the preconditioned method applied to Z-matrices is discussed. Also the optimal parameter is presented. Numerical results show that the proper choice of the preconditioner can lead to effective by the preconditioned Gauss-Seidel type iterative methods for solving linear systems.展开更多
In recent years, a number of preconditioners have been applied to solve the linear systems with Gauss-Seidel method (see [1-7,10-12,14-16]). In this paper we use Sl instead of (S + Sm) and compare with M. Morimoto’s ...In recent years, a number of preconditioners have been applied to solve the linear systems with Gauss-Seidel method (see [1-7,10-12,14-16]). In this paper we use Sl instead of (S + Sm) and compare with M. Morimoto’s precondition [3] and H. Niki’s precondition [5] to obtain better convergence rate. A numerical example is given which shows the preference of our method.展开更多
文摘For the linear least squares problem with coefficient matrix columns being highly correlated, we develop a greedy randomized Gauss-Seidel method with oblique direction. Then the corresponding convergence result is deduced. Numerical examples demonstrate that our proposed method is superior to the greedy randomized Gauss-Seidel method and the randomized Gauss-Seidel method with oblique direction.
基金Project supported by MOE's 2004 New Century Excellent Talent Program (NCET)the Applied Basic Research Foundations of Sichuan Province (No.05JY029-068-2)
文摘The preconditioned Gauss-Seidel type iterative method for solving linear systems, with the proper choice of the preconditioner, is presented. Convergence of the preconditioned method applied to Z-matrices is discussed. Also the optimal parameter is presented. Numerical results show that the proper choice of the preconditioner can lead to effective by the preconditioned Gauss-Seidel type iterative methods for solving linear systems.
文摘In recent years, a number of preconditioners have been applied to solve the linear systems with Gauss-Seidel method (see [1-7,10-12,14-16]). In this paper we use Sl instead of (S + Sm) and compare with M. Morimoto’s precondition [3] and H. Niki’s precondition [5] to obtain better convergence rate. A numerical example is given which shows the preference of our method.
