Abstract
We present a new subdivision strategy in interval analysis for computing the ranges of functions. We show through several real-world examples that the proposed subdivision strategy is more efficient than the widely used uniform and adaptive subdivision strategies of Moore (Methods and Applications of Interval Analysis, SIAM, Philadelphia, 1979).
Similar content being viewed by others
References
Ackermann, J.: Robust Control: Systems with Uncertain Physical Parameters, Springer-Verlag, 1975.
Ackermann, J. and Sienel, W.: On the Computation of Value Sets for Robust Stability Analysis, in: Proc. 1st European Control Conf., Grenoble, 1991, pp. 1345–1350.
Alefeld. G. and Herzberger, J.: Introduction to Interval Computations, Academic Press, New York, 1983.
Borghesani, C., Chait, Y., and Yaniv, O.: The Quantitative Feedback Theory Toolbox for MATLAB, 1995.
Chen, W. and Ballance, D. J.: Plant Template Generation for Uncertain Plants in QFT, Trans. of the ASME Journal of Dynamic Systems, Measurement and Control 121 (1999), pp. 359–364.
Forte Fortran 95 User Manual, Sun Microsystems, Palo Alto, 2001.
Horowitz, I.M.: Quantitative Feedback Design Theory (QFT), QFT Publications, Boulder, 1993.
Kearfott, R. B.: Some Tests of Generalized Bisection, ACM Transactions on Mathematical Software 13 (3) (1987), pp. 197–220.
MATLAB User Guide, version 5.3, The MathWorks Inc., 2000.
Moore, R. E.: Interval Analysis, Prentice Hall, Englewood Cliffs, 1966.
Moore, R. E.: Methods and Applications of Interval Analysis, SIAM, Philadelphia, 1979.
Nataraj, P. S. V. and Sardar, G.: Computation of QFT Bounds for Robust Sensitivity and Gain-Phase Margin Specifications, Trans. of the ASME Journal of Dynamic Systems, Measurement and Control 122 (2000), pp. 528–534.
Nataraj, P. S. V. and Sardar, G.: Template Generation for Continuous Transfer Functions Using Interval Analysis, Automatica 36 (2000), pp. 111–119.
Neumaier, A.: The Enclosure of Solutions of Parameter Dependent Systems of Equations, in: Moore, R. E. (ed.), Reliability in Computing: The Role of Interval Methods in Scientific Computations, Academic Press, 1988.
Rall, L. B.: Automatic Differentiation, Techniques and Applications, Lecture Notes in Computer Science 120, Springer-Verlag, Berlin, 1981.
Rodrigues, J. M., Chait, Y., and Hollot, C. V.: An Efficient Algorithm for Computing QFT Bounds, Trans. of the ASME Journal of Dynamic Systems, Measurement and Control 119 (3) (1997), pp. 548–552.
Rump, S. M.: INTLAB-Interval Laboratory, in: Csendes, T. (ed.), Developments in Reliable Computing, Kluwer Academic Publishers, 1999.
Sidi, M.: Feedback Synthesis with Plant Ignorance, Nonminimum Phase, and Time-Domain Tolerances, Automatica 12 (1976).
Thomspon, D. F. and Nwokah, O. D. I.: Analytical Loop Shaping Methods in Quantitative Feedback Theory, Trans. of the ASME Journal of Dynamic Systems, Measurement and Control 116 (1994), pp. 169–177.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nataraj, P.S.V., Sheela, S.M. A New Subdivision Strategy for Range Computations. Reliable Computing 8, 83–92 (2002). https://doi.org/10.1023/A:1014741703549
Issue Date:
DOI: https://doi.org/10.1023/A:1014741703549