Abstract
Many numerical problems are related to the study of the regularities of tridiagonal matrices. Recently, a series of sharp conditions for such matrices to be regular have been obtained through geometrical considerations and use of an associated three-term recurrence relation. In this note, we shall give an informal but organized presentation of the basic ideas behind, and highlight the excerpts from these results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. Bassett, J. Maybee, and J. Quirk, Qualitative economics and the scope of the correspondence principle, Econometrica 26 (1968), 544–563.
S.S. Cheng, A discrete analogue of the inequality of Lyapunov, Hakkaido Math. J., 12 (1983), 105–112.
S.S. Cheng, Sturmian comparison theorems for three-term recurrence equations, J. Math. Anal. Appl., 111 (1985), 464–474.
S.S. Cheng and T. T. Lu, Convex regular domains of tridiagonal matrices, Linear Algebra and its Appl., 79 (1986), 103–125.
S. S. Cheng, H. J. Li, T. T. Lu and S. H. Wu, Regular and singular orthants of tridiagonal matrices, Linear Algebra and its Appl., 94 (1987), 181–191.
S. S. Cheng, T. T. Lu and S. H. Wu, Regular starlike domains of tridiagonal matrices, preprint.
P. Hartman, Ordinary Differential Equations, Wiley, New York, 1964.
V. Klee, R. Ladner, and R. Manber, Signsolvability revisited, Lin. Alg. Appls. 59 (1984), 136–157.
J. Maybee and J. Quirk, Qualitative problems in matrix theory, SIAM Review 11 (1969), 30–51.
R. Mariber, Graph-theorectical approach to qualitative solvability of linear systems, Lin. Alg. Appls. 48 (1982), 457–470.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer Basel AG
About this chapter
Cite this chapter
Cheng, SS. (1988). Regular Domains of Tridiagonal Matrices. In: Agarwal, R.P., Chow, Y.M., Wilson, S.J. (eds) Numerical Mathematics Singapore 1988. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 86. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6303-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-0348-6303-2_9
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-2255-7
Online ISBN: 978-3-0348-6303-2
eBook Packages: Springer Book Archive