Expressions and bounds for the GMRES residual
The author discusses the generalized minimal residual method (GMRES) for the iterative solution of a linear system and derives expressions and bounds for the residual norm in this algorithm. The minimal residual norm is expressed in terms of the pseudo-inverse of the next Krylov matrix. The minimal residual norm of a scaled Jordan block is expressed in terms of the eigenvalues and deviation from normality. For normal matrices,the minimal residual norm is expressed in terms of products of the relative eigenvalue differences.
scientific article; zbMATH DE number 1533021
scientific article