Abstract
This paper studies convergence properties of the block gmres algorithm when applied to nonsymmetric systems with multiple right-hand sides. A convergence theory is developed based on a representation of the method using matrix-valued polynomials. Relations between the roots of the residual polynomial for block gmres and the matrix ε-pseudospectrum are derived, and illustrated with numerical experiments. The role of invariant subspaces in the effectiveness of block methods is also discussed.
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