02058585

j

02058585 Wang, Zhengsheng Adaptive block QMRIOM($q$) method for solving unsymmetric linear systems with multiple right-hand sides. Trans. Nanjing Univ. Aeronaut. Astronaut. 19, No. 1, 108-112 (2002). 2002 Nanjing University of Aeronautics \& Astronautics, Nanjing EN multiple right-hand sides block iterative methods large unsymmetric linear systems incomplete orthogonalization method block Krylov sequences Numerical experiments Summary: Many applications require the solution of large unsymmetric 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 orthogonalization method (IOM$(q))$ for solving large multiple unsymmetric linear systems. How to incorporate deflation to drop converged linear systems, and how to delete linearly and almost linearly dependent vectors in the underlying block Krylov sequences are discussed. Numerical experiments show that the new adaptive block method has better practical performance and less computational cost and CPU time than block GMRES and other proposed methods for the solution of systems with multiple right-hand sides.