On Overestimations Produced by the Interval Gaussian Algorithm
Tóm tắt
Interval Gaussian algorithm is a popular method for enclosing solutions of linear interval equations. In this note we show that both versions of the method (with or without preconditioning) may yield large overestimations for arbitrarily small data widths even in case n = 4.
Tài liệu tham khảo
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Neumaier, A.: Interval Methods for Systems of Equations, Cambridge University Press, Cambridge, 1990.
Reichmann, K.: Abbruch beim Intervall-Gauss-Algorithmus, Computing 22 (1979), pp. 355–361.
Rump, S. M.: Solving Algebraic Problems with High Accuracy, in: Kulisch, U. and Miranker, W. (eds), A New Approach to Scientific Computation, Academic Press, New York, 1983, pp. 51–120.