A block GMRES method augmented with eigenvectors

摘要

The GMRES method augmented with some eigenvectors is extended to a block version for solving large nonsymmetric linear systems with multiple right-hand sides. Residual bound is established which has an improved convergence rate on the standard block GMRES method. This improvement displays a good efficiency when restarting is used. Also an improved residual norm estimate is derived by using matrix-valued polynomials. Numerical experiments show that the new algorithm is more efficient, compared with the block GMRES method.