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Banded matrices and difference equations. (English) Zbl 1002.39028
The author considers finite difference equation versions of the Sturm-Liouville eigenvalue problems. He proves various results for such systems, in particular their relations to banded matrices.

39A12Discrete version of topics in analysis
39A10Additive difference equations
34L15Eigenvalues, estimation of eigenvalues, upper and lower bounds for OD operators
Full Text: DOI
[1] Berg, L.: Lineare gleichungssysteme mit bandstruktur. (1986) · Zbl 0613.15003
[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 · Zbl 0864.93026
[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, 804-826 (1996) · Zbl 0855.39018
[5] Bohner, M.: On disconjugacy for Sturm--Liouville difference equations. J. differential equations appl. 2, 227-237 (1996) · Zbl 0856.39019
[6] Bohner, M.; Došlý, O.: Positivity of blockridiagonal matrices. SIAM J. Matrix anal. Appl. 20, 182-195 (1999)
[7] M. Bohner, O. Došlý, W. Kratz, An oscillation theorem for discrete eigenvalue problems, to appear · Zbl 1060.39003
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[10] Horn, R. A.; Johnson, C. A.: Matrix analysis. (1991) · Zbl 0729.15001
[11] Kratz, W.: Quadratic functionals in variational analysis and control theory. (1995) · Zbl 0842.49001
[12] Reid, W. T.: Sturmian theory for ordinary differential equations. (1980) · Zbl 0459.34001
[13] Schwarz, H. R.; Rutishauser, H.; Stiefel, E.: Numerik symmetrischer matrizen. (1972)
[14] Wilkinson, J. H.: The algebraic eigenvalue problem. (1965) · Zbl 0258.65037