We are interested in the numerical solution of the large nonsymmetric shifted linear system, （A ＋ αI）x -= b, for many different values of the shift a in a wide range. We apply the Saad＇s flexible preconditioning ...We are interested in the numerical solution of the large nonsymmetric shifted linear system, （A ＋ αI）x -= b, for many different values of the shift a in a wide range. We apply the Saad＇s flexible preconditioning technique to the solution of the shifted systems. Such flexible preconditioning with a few parameters could probably cover all the shifted systems with the shift in a wide range. Numerical experiments report the effectiveness of our approach on some problems.展开更多
In this paper,we study shifted restated full orthogonalization method with deflation for simultaneously solving a number of shifted systems of linear equations.Theoretical analysis shows that with the deflation techni...In this paper,we study shifted restated full orthogonalization method with deflation for simultaneously solving a number of shifted systems of linear equations.Theoretical analysis shows that with the deflation technique,the new residual of shifted restarted FOM is still collinear with each other.Hence,the new approach can solve the shifted systems simultaneously based on the same Krylov subspace.Numerical experiments show that the deflation technique can significantly improve the convergence performance of shifted restarted FOM.展开更多
基金Research supported by the National Natural Science Foundation of China （10271075）.
文摘We are interested in the numerical solution of the large nonsymmetric shifted linear system, （A ＋ αI）x -= b, for many different values of the shift a in a wide range. We apply the Saad＇s flexible preconditioning technique to the solution of the shifted systems. Such flexible preconditioning with a few parameters could probably cover all the shifted systems with the shift in a wide range. Numerical experiments report the effectiveness of our approach on some problems.
文摘In this paper,we study shifted restated full orthogonalization method with deflation for simultaneously solving a number of shifted systems of linear equations.Theoretical analysis shows that with the deflation technique,the new residual of shifted restarted FOM is still collinear with each other.Hence,the new approach can solve the shifted systems simultaneously based on the same Krylov subspace.Numerical experiments show that the deflation technique can significantly improve the convergence performance of shifted restarted FOM.
