Summary
Error bounds are given for the iterative computation of the eigenvectors in the Rayleigh-Schrödinger series. These bounds remove the discrepancy in the theoretical behaviour and numerical results, noted by Redont, under the assumption of collectively compact convergence. As a particular case, it follows that the eigenvector in the iterative Galerkin method proposed by Sloan improves upon the eigenvector in the Galerkin method. This is illustrated by numerical experiments.
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References
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Work supported in part by a grant from the Council of Scientific and Industrial Research, New Delhi, India
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Kulkarni, R.P., Limaye, B.V. On the steps of convergence of approximate eigenvectors in the Rayleigh-Schrödinger series. Numer. Math. 42, 31–50 (1983). https://doi.org/10.1007/BF01400916
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DOI: https://doi.org/10.1007/BF01400916