A block EN algorithm for nonsymmetric linear systems with multiple right-hand sides Original Research Article

The EN method proposed by Eirola and Nevanlinna is extended to a block version for solving nonsymmetric linear systems with multiple right-hand sides. Some basic properties of the block-EN method are shown. We use the deflation technique in the block-EN method to delete linearly dependent vectors in the underlying block sequences and drop the corresponding linear systems or converged linear systems. However, our BEN method with deflation procedure still keeps the blockwise computation, instead of vectorwise generation of the basis vectors for the underlying block subspace. Numerical experiments show that the algorithm is efficient and robust.