Convergence properties of block GMRES and matrix polynomials Original Research Article

This paper studies convergence properties of the block image 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 image and the matrix var epsilon-pseudospectrum are derived, and illustrated with numerical experiments. The role of invariant subspaces in the effectiveness of block methods is also discussed.