Expressions and Bounds for the GMRES Residual |
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| Authors: | I C F Ipsen |
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| Institution: | (1) Department of Mathematics, North Carolina State University, Raleigh, NC, 27695-8205, USA. |
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| Abstract: | Expressions and bounds are derived for the residual norm in GMRES. It is shown that the minimal residual norm is large as long as the Krylov basis is well-conditioned. For scaled Jordan blocks the minimal residual norm is expressed in terms of eigenvalues and departure from normality. For normal matrices the minimal residual norm is expressed in terms of products of relative eigenvalue differences. |
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| Keywords: | Linear system Krylov space methods GMRES MINRES Vandermonde matrix eigenvalues departure from normality |
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