Abstract
We derive a linear system for the midpoint and the radius of the limit [xl* of the interval total step method [x]k+1 = [A][x]k +[b] provided that p(|[A]|) < 1. The coefficients of this system are formed by lower and upper bounds of the input intervals, their choice depends on the position of the components of [x](vn*) with respect to zero. For particular input data this choice can be made without knowing [x](vn*). For nonnegative [A] the coefficients are determined by solving at most n + 1 real linear systems.
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References
Alefeld, G., Herzberger, J. (1983) Introduction to Interval Computations. Academic Press, New York
Barth, W., Nuding, E. (1974) Optimale Lösung von Intervallgleichungssystemen. Computing 12, 117–125
Kulisch, U. (1969) Grundzüge der Intervallrechnung. In: Laugwitz, L. (Ed.) Überblicke Mathematik 2. Bibliographisches Institut, Mannheim, 51–98
Mayer, G, Warnke, I. (2001) On the Shape of the Fixed Points of [f]([x]) = [A][x] + [b]. In: Alefeld, G., Rohn, J., Rump, S. M., Yamamoto, T. (Eds.): Symbolie Aigebraie Methods and Verifieation Methods- Theory and Applieations. Springer, Wien, to appear
Mayer, G, Warnke, 1., On the Fixed Points of the Interval Function [J]([x]) = [A][x] + [b]. Submitted for publieation.
Mayer, O. (1968) Über die in der Intervallreehnung auftretenden Räume und einige Anwendungen. Ph.D. Thesis, Universität Karlsruhe, Karlsruhe
Neumaier, A. (1990) Interval Methods for Systems of Equations. Cambridge University Press, Cambridge
Varga, R. S. (1962) Matrix Iterative Analysis. Prentiee-Hall, Englewood Cliffs, N.J.
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© 2001 Springer-Verlag Wien
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Mayer, G., Warnke, I. (2001). On the Limit of the Total Step Method in Interval Analysis. In: Kulisch, U., Lohner, R., Facius, A. (eds) Perspectives on Enclosure Methods. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6282-8_9
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DOI: https://doi.org/10.1007/978-3-7091-6282-8_9
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83590-6
Online ISBN: 978-3-7091-6282-8
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