Abstract
Generalized intervals (intervals whose bounds are not constrained to be increasingly ordered) extend classical intervals providing better algebraic properties. In particular, the generalized interval arithmetic is a group for addition and for multiplication of zero free intervals. These properties allow one constructing a LU decomposition of a generalized interval matrix A: the two computed generalized interval matrices L and U satisfy A = LU with equality instead of the weaker inclusion obtained in the context of classical intervals. Some potential applications of this generalized interval LU decomposition are investigated.
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
Neumaier, A.: Interval Methods for Systems of Equations. Cambridge University Press, Cambridge (1990)
Ortolf, H.J.: Eine Verallgemeinerung der Intervallarithmetik, vol. 11, pp. 1–71. Geselschaft fuer Mathematik und Datenverarbeitung, Bonn (1969)
Kaucher, E.: Uber metrische und algebraische Eigenschaften einiger beim numerischen Rechnen auftretender Raume. PhD thesis, Karlsruhe (1973)
Kaucher, E.: Interval Analysis in the Extended Interval Space \(\mathbb{IR}\). Computing, Suppl. 2, 33–49 (1980)
Shary, S.: A new technique in systems analysis under interval uncertainty and ambiguity. Reliable computing 8, 321–418 (2002)
Popova, E.: Multiplication distributivity of proper and improper intervals. Reliable computing 7(2), 129–140 (2001)
SIGLA/X group: Modal intervals. Reliab. Comp. 7, 77–111 (2001)
Goldsztejn, A., Chabert, G.: On the approximation of linear AE-solution sets. In: 12th GAMM – IMACS International Symposion on Scientific Computing, Duisburg, Germany (2006)
Shary, S.: Interval Gauss-Seidel Method for Generalized Solution Sets to Interval Linear Systems. Reliable computing 7, 141–155 (2001)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Goldsztejn, A., Chabert, G. (2007). A Generalized Interval LU Decomposition for the Solution of Interval Linear Systems. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2006. Lecture Notes in Computer Science, vol 4310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70942-8_37
Download citation
DOI: https://doi.org/10.1007/978-3-540-70942-8_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70940-4
Online ISBN: 978-3-540-70942-8
eBook Packages: Computer ScienceComputer Science (R0)