Abstract
This paper is motivated by the paper [7], where the SOR method for solving linear interval equations was considered. It is known that sometimes the AOR method for systems of linear (“point”) equations converges faster than the SOR method. We give some sufficient conditions for the convergence of the interval AOR method for the same class of interval matrices which are considered in [7].
Zusammenfassung
Diese Arbeit ist durch die Arbeit [7] motiviert, wo das SOR-Verfahren zur Lösung von linearen Intervallgleichungen betrachtet wird. Es ist bekannt, daß das AOR-Verfahren für lineare (“Punkt”) Gleichungssysteme manchmal schneller als das SOR-Verfahren konvergiert. Wir geben einige hinreichende Konvergenzbedingungen für das Intervall-AOR-Verfahren für dieselbe Klasse von Matrizen, die in [7] betrachtet wurde.
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Cvetković, Lj.: On the nonsingularity of interval matrices. In: Conference on Applied Mathematics (Bohte, Z., ed.), pp. 27–32. Ljubljana: University of Ljubjana, Institute of Mathematics, Physics and Mechanics 1986.
Cvetković, Lj., Herceg, D.: Convergence theory for AOR method. Journal of Computational Mathematics (to appear).
Cvetković, Lj., Herceg, D.: An improvement for the area of convergence of the AOR method. Anal. Numer. Theor. Approx.16, 109–115 (1987).
Hadjidimos, A.: Accelerated overrelaxation method. Math. Comp.32, 149–157 (1978).
Neumaier, A.: New techniques for the analysis of linear interval equations. Linear Algebra and its Applications58, 273–325 (1984).
Neumaier, A.: Further results on linear interval equations. Freiburger Intervall-Berichte85/4, 37–72 (1985).
Qingrong, L., Zhiying, J.: The SOR method for solving linear interval equations. Freiburger Interval-Berichte87/7, 1–7 (1987).
Author information
Authors and Affiliations
Additional information
This research was partly supported by NSF and SIZ for Science of SAP Vojvodina through funds made available to the U.S.-Yugoslav Joint Board on Scientific and Technological Cooperation (grant JF 799).
Rights and permissions
About this article
Cite this article
Cvetković, L., Herceg, D. The AOR method for solving linear interval equations. Computing 41, 359–364 (1989). https://doi.org/10.1007/BF02241224
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02241224