Can We Improve the Standard Algorithm of Interval Computation by Taking Almost Monotonicity into Account?

  • Martine Ceberio
  • Olga Kosheleva
  • Vladik KreinovichEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1000)


In many practical situations, it is necessary to perform interval computations – i.e., to find the range of a given function \(y=f(x_1,\ldots ,x_n)\) on given intervals – e.g., when we want to find guaranteed bounds of a quantity that is computed based on measurements, and for these measurements, we only have upper bounds of the measurement error. The standard algorithm for interval computations first checks for monotonicity. However, when the function f is almost monotonic, this algorithm does not utilize this fact. In this paper, we show that such closeness-to-monotonicity can be efficiently utilized.



This work was supported in part by the US National Science Foundation grant HRD-1242122 (Cyber-ShARE Center of Excellence).


  1. 1.
    Jaulin, L., Kiefer, M., Didrit, O., Walter, E.: Applied Interval Analysis, with Examples in Parameter and State Estimation, Robust Control, and Robotics. Springer, London (2001). Scholar
  2. 2.
    Kreinovich, V., Lakeyev, A., Rohn, J., Kahl, P.: Computational Complexity and Feasibility of Data Processing and Interval Computations. Kluwer, Dordrecht (1998)CrossRefGoogle Scholar
  3. 3.
    Mayer, G.: Interval Analysis and Automatic Result Verification. de Gruyter, Berlin (2017)CrossRefGoogle Scholar
  4. 4.
    Moore, R.E., Kearfott, R.B., Cloud, M.J.: Introduction to Interval Analysis. SIAM, Philadelphia (2009)CrossRefGoogle Scholar
  5. 5.
    Rabinovich, S.G.: Measurement Errors and Uncertainties: Theory and Practice. Springer, New York (2005)zbMATHGoogle Scholar
  6. 6.
    Vavasis, S.A.: Nonlinear Optimization: Complexity Issues. Oxford University Press, New York (1991)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Martine Ceberio
    • 1
  • Olga Kosheleva
    • 2
  • Vladik Kreinovich
    • 1
    Email author
  1. 1.Department of Computer ScienceUniversity of Texas at El PasoEl PasoUSA
  2. 2.Department of Teacher EducationUniversity of Texas at El PasoEl PasoUSA

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