Banded matrices and difference equations

Linear Algebra and Its Applications

Volumn 337, Issue 1-3, 2001, Pages 1-20

  Kratz, Werner ^a  

^a UNIVERSITY OF ULM   (Germany)

Author keywords

15A18; 39A10; 39A12; 65F15; Banded matrices; Discrete oscillation; Hamiltonian difference systems; Jacobi's formula; Picone's identity; Poincar separation theorem; Sturm Liouville equations; Sturmian chains; Symmetric eigenvalue problem

Indexed keywords

EID: 0035501552     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(01)00328-7     Document Type: Article

References (14)

1. Berg L. Lineare Gleichungssysteme mit Bandstruktur. 1986;Carl Hanser, München.
2. M. Bohner, Controllability and disconjugacy for linear Hamiltonian difference systems, in: Proceedings of the First International Conference on Difference Equations, San Antonio, 1994, pp. 65-77.
3. M. Bohner, Zur Positivität diskreter quadratischer Funktionale, Dissertation, Ulm, 1995.
4. Bohner M. Linear Hamiltonian difference systems: disconjugacy and Jacobi-type conditions. J. Math. Anal. Appl. 199:1996;804-826.
5. Bohner M. On disconjugacy for Sturm-Liouville difference equations. J. Differential Equations Appl. 2:1996;227-237.
6. Bohner M., Došlý O. Positivity of blockridiagonal matrices. SIAM J. Matrix Anal. Appl. 20:1999;182-195.
7. M. Bohner, O. Došlý, W. Kratz, An oscillation theorem for discrete eigenvalue problems, to appear.
8. F.R. Gantmacher, The Theory of Matrices, vol. 1, Chelsea, New York, 1959 (originally published in Moscow, 1954).
9. Golub G.H., Van Loan C.F. Matrix Computations. 1983;John Hopkins University Press, Baltimore, MD.
10. Horn R.A., Johnson C.A. Matrix Analysis. 1991;Cambridge University Press, Cambridge.
11. Kratz W. Quadratic Functionals in Variational Analysis and Control Theory. 1995;Akademie, Berlin.
12. Reid W.T. Sturmian Theory for Ordinary Differential Equations. 1980;Springer, New York.
13. Schwarz H.R., Rutishauser H., Stiefel E. Numerik symmetrischer Matrizen. 1972;Teubner, Stuttgart.
14. Wilkinson J.H. The Algebraic Eigenvalue Problem. 1965;Clarendon Press, Oxford, UK.