Abstract
We generalize and extend results of the series of papers by Greenbaum and Strakoš (IMA Vol Math Appl 60:95–118, 1994), Greenbaum et al. (SIAM J Matrix Anal Appl 17(3):465–469, 1996), Arioli et al. (BIT 38(4):636–643, 1998) and Duintjer Tebbens and Meurant (SIAM J Matrix Anal Appl 33(3):958–978, 2012). They show how to construct matrices with right-hand sides generating a prescribed GMRES residual norm convergence curve as well as prescribed Ritz values in all iterations, including the eigenvalues, and give parametrizations of the entire class of matrices and right-hand sides with these properties. These results assumed that the underlying Arnoldi orthogonalization processes are breakdown-free and hence considered non-derogatory matrices only. We extend the results with parametrizations of classes of general nonsingular matrices with right-hand sides allowing the early termination case and also give analogues for the early termination case of other results related to the theory developed in the papers mentioned above.
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Duintjer Tebbens, J., Meurant, G. Prescribing the behavior of early terminating GMRES and Arnoldi iterations. Numer Algor 65, 69–90 (2014). https://doi.org/10.1007/s11075-013-9695-x
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DOI: https://doi.org/10.1007/s11075-013-9695-x