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Variants of the Block-GMRES Method for Solving Linear Systems with Multiple Right-Hand Sides

The solution of large linear systems with multiple right-hand sides given simultaneously is required in many large-scale scientific and engineering applications modelled by either partial differential or boundary integral equations. In this paper we introduce variants of the block GMRES method that combine initial deflation and eigenvalue recycling strategies to remedy some typical convergence problems of block Krylov solvers.