The symmetric linear system gives us many simplifications and a possibility to adapt the computations to the computer at hand in order to achieve better performance. The aim of this paper is to consider the block bidi...The symmetric linear system gives us many simplifications and a possibility to adapt the computations to the computer at hand in order to achieve better performance. The aim of this paper is to consider the block bidiagonalization methods derived from a symmetric augmented multiple linear systems and make a comparison with the block GMRES and block biconjugate gradient methods.展开更多
Many applications require the solution of large un-symmetric linear systems with multiple right-hand sides.Instead of applying an iterative method to each of these systems individually,it is often more efficient to us...Many applications require the solution of large un-symmetric linear systems with multiple right-hand sides.Instead of applying an iterative method to each of these systems individually,it is often more efficient to use a block version of the method that generates iterates for all the systems simultaneously.This paper proposes a new adaptive block QMR version based on the incomplete or-thogomalization method(IOM(q))for solving large multi-ple nusymmetric linear systems.How to incorporate de-flation to drop comverged linear systems,and how to delete linearly and almost liearly dependent vectors in the underlying block Krylov sequences are discussed.Nu-merical experiments show that the new adaptive block method has better practical performance and less compu-tational cost and CPU time than block GMRES and other proposed methods for the solution of systems with multi- ple right-hand sides.展开更多
We consider using seed projection methods for solving unsymmetric shifted systems with multiple right-hand sides (A - σjI)x^(j) = b^(j) for 1 ≤ j ≤ p. The methods use a single Krylov subspace corresponding to a see...We consider using seed projection methods for solving unsymmetric shifted systems with multiple right-hand sides (A - σjI)x^(j) = b^(j) for 1 ≤ j ≤ p. The methods use a single Krylov subspace corresponding to a seed system as a generator of approximations to the nonseed systems. The residual evaluates of the methods are given. Finally, numerical results are reported to illustrate the effectiveness of the methods.展开更多
基金The research of this author was supported by the National Natural Science Foundation of China,the JiangsuProvince Natural Science Foundation,the Jiangsu Province"333Engineering" Foundation and the Jiangsu Province"Qinglan Engineering" Foundation
文摘The symmetric linear system gives us many simplifications and a possibility to adapt the computations to the computer at hand in order to achieve better performance. The aim of this paper is to consider the block bidiagonalization methods derived from a symmetric augmented multiple linear systems and make a comparison with the block GMRES and block biconjugate gradient methods.
文摘Many applications require the solution of large un-symmetric linear systems with multiple right-hand sides.Instead of applying an iterative method to each of these systems individually,it is often more efficient to use a block version of the method that generates iterates for all the systems simultaneously.This paper proposes a new adaptive block QMR version based on the incomplete or-thogomalization method(IOM(q))for solving large multi-ple nusymmetric linear systems.How to incorporate de-flation to drop comverged linear systems,and how to delete linearly and almost liearly dependent vectors in the underlying block Krylov sequences are discussed.Nu-merical experiments show that the new adaptive block method has better practical performance and less compu-tational cost and CPU time than block GMRES and other proposed methods for the solution of systems with multi- ple right-hand sides.
文摘We consider using seed projection methods for solving unsymmetric shifted systems with multiple right-hand sides (A - σjI)x^(j) = b^(j) for 1 ≤ j ≤ p. The methods use a single Krylov subspace corresponding to a seed system as a generator of approximations to the nonseed systems. The residual evaluates of the methods are given. Finally, numerical results are reported to illustrate the effectiveness of the methods.
