Convergence of LR algorithm for a one-point spectrum tridiagonal matrix
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.
Mathematics Subject Classification (2000)65F15
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- 1.Demmel, J.W.: Applied Numerical Linear Algebra. Society for Industrial and Applied Mathematics, Philadelphia (1997)Google Scholar
- 3.Horn R.A., Johnson C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1996)Google Scholar
- 4.Liu Z.S. (1992) On the extended HR algorithm. Technical Report PAM-564, Center for Pure and Applied Mathematics, University of California, Berkeley, CA, USA (1992)Google Scholar
- 8.Parlett, B.N.: What Hadamard Missed. Unpublished Technical Report (1996)Google Scholar