Numerische Mathematik

, Volume 113, Issue 3, pp 417–431

Convergence of LR algorithm for a one-point spectrum tridiagonal matrix

Open AccessArticle

DOI: 10.1007/s00211-009-0238-2

Cite this article as:
Ferreira, C. & Parlett, B. Numer. Math. (2009) 113: 417. doi:10.1007/s00211-009-0238-2


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)

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© The Author(s) 2009

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of MinhoBragaPortugal
  2. 2.Department of Mathematics and the Computer Science Division of the Electrical Engineering and Computer Science DepartmentUniversity of CaliforniaBerkeleyUSA