article · 2015

CONVERGENCE OF LR FOR A ONE-POINT SPECTRUM TRIDIAGONAL MATRIX

Carla Ferreira, Beresford Parlett

Cited by 0Abstract and details only

Abstract

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 develope properties of eigenvector matrices. Key words. unsymmetric tridiagonal matrices, multiple eigenvalues, LR algorithm AMS subject classifications. 65F15 1. Introduction. This paper presents a rigorous proof that the LR algorithm, without shifts, applied to an unreduced tridiagonal matrix with a one-point spectrum converges to an upper bidi-agonal matrix. The rate of convergence is very slow, like 1/k after k steps, but what is remarkable is that the algorithm actually converges. We hasten to say that this result is not exactly new. In the middle of the 1960’s J.H. Wilkinson sketched out the underlying reason for this surprising result,

Cite this paper

APA 7

Ferreira, C., & Parlett, B. (2015). CONVERGENCE OF LR FOR A ONE-POINT SPECTRUM TRIDIAGONAL MATRIX.

MLA 9

Ferreira, Carla, and Beresford Parlett. “CONVERGENCE OF LR FOR A ONE-POINT SPECTRUM TRIDIAGONAL MATRIX.” 2015.

Chicago

Ferreira, Carla, and Beresford Parlett. 2015. “CONVERGENCE OF LR FOR A ONE-POINT SPECTRUM TRIDIAGONAL MATRIX.”

Harvard

Ferreira, C. and Parlett, B. (2015) ‘CONVERGENCE OF LR FOR A ONE-POINT SPECTRUM TRIDIAGONAL MATRIX’.

BibTeX

@article{ferreira2015convergence,
  title = {{CONVERGENCE OF LR FOR A ONE-POINT SPECTRUM TRIDIAGONAL MATRIX}},
  author = {Ferreira, Carla and Parlett, Beresford},
  year = {2015}
}

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