This article is cited in 7 papers

General numerical methods

Computing the eigenvectors of nonsymmetric tridiagonal matrices

P. Van Dooren^a, T. Laudadio^b, N. Mastronardi<sup>b

a</sup> Department of Mathematical Engineering, Catholic University of Louvain, Louvain-la-Neuve, Belgium
^b Istituto per le Applicazioni del Calcolo, Bari, Italy

Abstract: The computation of the eigenvalue decomposition of matrices is one of the most investigated problems in numerical linear algebra. In particular, real nonsymmetric tridiagonal eigenvalue problems arise in a variety of applications. In this paper the problem of computing an eigenvector corresponding to a known eigenvalue of a real nonsymmetric tridiagonal matrix is considered, developing an algorithm that combines part of a $QR$ sweep and part of a $QL$ sweep, both with the shift equal to the known eigenvalue. The numerical tests show the reliability of the proposed method.

Key words: nonsymmetric tridiagonal matrices, eigenvectors, Bessel matrices.

UDC: 519.61

Received: 24.11.2020
Revised: 24.11.2020
Accepted: 14.01.2021

DOI: 10.31857/S0044466921050082

 English version: Computational Mathematics and Mathematical Physics, 2021, 61:5, 733–749

Bibliographic databases:

• 
• 
•