Abstract
We will discuss some modifications of the interval Gauss algorithm, so that it becomes feasible in a more general setting, particularly for totally non-negative matrices.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alefeld, G. and Herzberger, J.: Introduction to Interval Computations, Academic Press, New York, 1983.
Ando, T.: Totally Positive Matrices, Linear Algebra and Its Applications 90 (1987), pp. 165–219.
Craven, T. and Csordas, G.: A Sufficient Condition for Strict Total Positivity of a Matrix, Linear and Multilinear Algebra 45 (1998), pp. 19–34.
Gantmacher, F.: Matrizentheorie, Springer Verlag, Berlin, 1986.
Gasca, M. and Micchelli, C.: Total Positivity and Its Applications, Kluwer Academic Publishers, Dordrecht, 1996.
Gasca, M. and Peña, J. M.: Total Positivity and Neville Elimination, Linear Algebra and Its Applications 165 (1992), pp. 25–44.
Garloff, J.: Totally Nonnegative Interval Matrices, in: Nickel, K., Interval Mathematics 1980, Academic Press, New York, 1980, pp. 317–327.
Karlin, S.: Total Positivity, Stanford University Press, Stanford, 1968.
Mayer, G.: Old and New Aspects of the Interval Gaussian Algorithm, in: Kaucher, E., Markov, S., and Mayer, G., IMACS Annals on Computing and Applied Mathematics, Baltzer, Basel, 1992, pp. 329–349.
Reichmann, K.: Abbruch beim Interval-Gauss-Algorithmus, Computing 22 (1979), pp. 355–361.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mayer, J. An Approach to Overcome Division by Zero in the Interval Gauss Algorithm. Reliable Computing 8, 229–237 (2002). https://doi.org/10.1023/A:1015565313636
Issue Date:
DOI: https://doi.org/10.1023/A:1015565313636