Hostname: page-component-7bb8b95d7b-s9k8s Total loading time: 0 Render date: 2024-09-18T03:41:46.608Z Has data issue: false hasContentIssue false

A formula for Eigenpairs of certain symmetric tridiagonal matrices

Published online by Cambridge University Press:  17 April 2009

Byeong Chun Shin
Affiliation:
Department of Mathematics, Kyungpook National University, Taegu 702–701, Korea
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A closed form expression is given for the eigenvalues and eigenvectors of a symmetric tridiagonal matrix of odd order whose diagonal elements are all equal and whoes superdiagonal elements alternate between the values c and d. An implicit formula is given for the even order case.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Arbenz, P., ‘Computing eigenvalues of banded symmetric Toeplitz matrices’, Z. Angew. Math. Mech. 70 (1990), 595597.Google Scholar
[2]Arbenz, P., ‘Computing eigenvalues of banded symmetric matrices’, SIAM J. Sci. Statist. Comput. 12 (1991), 743754.Google Scholar
[3]Kim, S.D. and Parter, S.V., ‘Preconditioning cubic spline collocation discretizations of elliptic equations’, Numer. Math. 72 (1995), 3972.Google Scholar
[4]Trench, W.F., ‘A note on computing eigenvalues of banded Hermitian Toeplitz matrices’, SIAM J. Sci. Statist. Comput. 14 (1993), 248252.Google Scholar
[5]Trench, W.F., ‘On the eigenvalue problem for Toeplitz band matrices’, Appl. 64 (1985), 199214.Google Scholar