Abstract
We prove convergence for the basic LR algorithm on a real unreduced tridiagonal matrix with a one-point spectrum—the Jordan form is one big Jordan block. First we develop properties of eigenvector matrices. We also show how to deal with the singular case.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Ferreira, C., Parlett, B. Convergence of LR algorithm for a one-point spectrum tridiagonal matrix. Numer. Math. 113, 417–431 (2009). https://doi.org/10.1007/s00211-009-0238-2
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DOI: https://doi.org/10.1007/s00211-009-0238-2