Article contents
EXPLICIT EIGENVALUES AND INVERSES OF TRIDIAGONAL TOEPLITZ MATRICES WITH FOUR PERTURBED CORNERS
Part of:
Basic linear algebra
Published online by Cambridge University Press: 01 January 2008
Abstract
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.
By means of a symbolic calculus for finding solutions of difference equations, we derive explicit eigenvalues, eigenvectors and inverses for tridiagonal Toeplitz matrices with four perturbed corners.
MSC classification
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 2008
References
[1]Cheng, S. S., Partial difference equations (Taylor and Francis, London, 2003).CrossRefGoogle Scholar
[2]Cheng, S. S. and Hsieh, L. Y., “Inverses of matrices arising from difference operators”, Util. Math. 38 (1990) 65–77.Google Scholar
[3]Dow, M., “Explicit inverses of Toeplitz and associated matrices”, ANZIAM J. 44 (2003) 185–215.CrossRefGoogle Scholar
[4]Gohberg, I. C. and Semencul, A. A., “On the inversion of finite Toeplitz matrices and their continuous analogs”, Mat. Issled 7 (1972) 201–223 (in Russian).Google Scholar
[5]Haley, S. B., “Solutions of band matrix equations by projection-recurrence”, Linear Algebra Appl. 32 (1980) 33–48.CrossRefGoogle Scholar
[6]Householder, A. S., The theory of matrices in numerical analysis (Dover Publications, New York, 1975).Google Scholar
[7]Trench, W. F., “An algorithm for the inversion of finite Toeplitz matrices”, SIAM J. Appl. Math. 12 (1964) 515–522.CrossRefGoogle Scholar
[8]Yueh, W. C., “Eigenvalues of several tridiagonal matrices”, Appl. Math. E-Notes 5 (2005) 66–74.Google Scholar
[9]Yueh, W. C., “Explicit inverses of several tridiagonal matrices”, Appl. Math. E-Notes 6 (2006) 74–83.Google Scholar
[10]Yueh, W. C. and Cheng, S. S., “Explicit eigenvalues and inverses of several Toeplitz matrices”, ANZIAM J. 48 (2006) 73–97.CrossRefGoogle Scholar
You have
Access
- 50
- Cited by