Abstract
Second-order enc10sures for a function’s range can be computed with centered forms, which involve a so-called slope vector. In this paper we discuss several techniques for determining such vectors and compare them with respect to tightness of the resulting enc1osure. We advocate that a two-stage slope vector computation with symbolic preprocessing is optimal.
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References
G. Alefeld and J. Herzberger. Introduetion to Interval Gomputations. Academic Press, New York, NY, 1983.
C. Bischof, A. Carle, P. Hovland, P. Khademi, and A. Mauer. ADIFOR 2.0 user’s guide. Technical Memorandum ANL/MCS-TM-192, Argonne National Laboratory, Mathematics and Computer Science Division, 1995. Revised June 1998.
C. Bliek. Fast evaluation of partial derivatives and interval slopes. Reliable Comput., 3:259–268, 1997.
G. F. Corliss and L. B. Rall. Adaptive, self-validating quadrature. SIAM J. Sei. Stat. Comput., 8(5):831–847, 1987.
A. Griewank. Evaluating Derivatives: Prineiples and Teehniques of Algorithmie Differentiation. Frontiers in Applied Mathematics. SIAM, Philadelphia, PA, 2000.
R. B. Kearfott. Rigorous Global Seareh: Continuous Problems. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
A. Neumaier. Interval Methods for Systems of Equations. Cambridge University Press, Cambridge, UK, 1990.
J. B. Oliveira. New slope methods for sharper interval functions and a note on Fischer’s acceleration method. Reliable Comput., 2(3):299–320, 1996.
L. B. Rall. Automatie Differentiation: Teehniques and Applieations. Lecture Notes in Computer Science, No. 120. Springer-Verlag, Berlin, Germany, 1981.
D. Ratz. Automatie Slope Computation and its Applieation in Nonsmooth Global Optimization. Shaker Verlag, Aachen, Germany, 1998. Habilitationsschrift.
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© 2001 Springer-Verlag Wien
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Lang, B. (2001). A Comparison of Techniques for Evaluating Centered Forms. In: Kulisch, U., Lohner, R., Facius, A. (eds) Perspectives on Enclosure Methods. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6282-8_8
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DOI: https://doi.org/10.1007/978-3-7091-6282-8_8
Publisher Name: Springer, Vienna
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