Tridiagonal test matrices for eigenvalue computations: two-parameter extensions of the Clement matrix
Abstract
The Clement or Sylvester-Kac matrix is a tridiagonal matrix with zero diagonal and simple integer entries. Its spectrum is known explicitly and consists of integers which makes it a useful test matrix for numerical eigenvalue computations. We consider a new class of appealing two-parameter extensions of this matrix which have the same simple structure and whose eigenvalues are also given explicitly by a simple closed form expression. The aim of this paper is to present in an accessible form these new matrices and examine some numerical results regarding the use of these extensions as test matrices for numerical eigenvalue computations.
Cite
@article{arxiv.1612.07619,
title = {Tridiagonal test matrices for eigenvalue computations: two-parameter extensions of the Clement matrix},
author = {Roy Oste and Joris Van der Jeugt},
journal= {arXiv preprint arXiv:1612.07619},
year = {2016}
}
Comments
This is a preprint of a paper whose final and definite form is in Journal of Computational and Applied Mathematics