Balanced Random and Adaptive Interval Arithmetic for Systems of Linear Interval Equations

  • J. Žilinskas
  • I. D. L. Bogle
Conference paper


The paper concerns interval methods — valuable tools for solving engineering problems — for finding outer approximations for the solution set of systems of linear interval equations. The paper shows how interval methods are used to analyse steady-state concentrations of systems of coupled reactors. The results of the experiments evaluating the outer approximations for the solution set of systems of linear interval equations using Gaussian elimination with standard and balanced random interval arithmetic are given. Adaptive interval arithmetic is proposed to overcome disadvantages of balanced random interval arithmetic.


Gaussian Elimination Interval Arithmetic Random Coefficient Interval Method Outer Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Moore RE, (1966) Interval Analysis. Prentice Hall.Google Scholar
  2. 2.
    Hansen E, (1992) Global Optimization using Interval Analysis. Marcel Dekker.Google Scholar
  3. 3.
    Gau CY, Stadtherr MA, (2002) New Interval Methodologies for Reliable Chemical Process Modeling. Computers and Chemical Engineering, 26(6); 827–840.CrossRefGoogle Scholar
  4. 4.
    Byrne RP, Bogle IDL, (1999) Global Optimization of Constrained Non-convex Programs using Reformulation and Interval Analysis. Computers and Chemical Engineering, 23(9); 1341–1350.CrossRefGoogle Scholar
  5. 5.
    Adjiman CS, (1999) Safety Verification in Chemical Plants: A New Quantitative Approach. Computers and Chemical Engineering, 23 Supplement; S581–S584.CrossRefGoogle Scholar
  6. 6.
    Chapra SC, Canale RP, (2002) Numerical Methods for Engineers: with Software and Programming Applications — 4th ed. McGraw-Hill.Google Scholar
  7. 7.
    Zilinskas J, Bogle IDL, (2003) On the Generalization of a Random Interval Method. In: European Symposium on Computer Aided Process Engineering — 13, Lappeenranta, Finland; 989–994.Google Scholar
  8. 8.
    Alt R, Lamotte JL, (2001) Experiments on the Evaluation of Functional Ranges using Random Interval Arithmetic. Mathematics and Computers in Simulation, 56(1); 17–34.MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Zilinskas J, Bogle IDL, (2003) Evaluation Ranges of Functions using Balanced Random Interval Arithmetic. Informatica, 14(3); 403–416.MathSciNetMATHGoogle Scholar
  10. 10.
    Neumaier A, (1990) Interval Methods for Systems of Equations. Cambridge University Press.Google Scholar
  11. 11.
    Jaulin L, Kieffer M, Didrit O, Walter E, (2001) Applied Interval Analysis. Springer-Verlag.Google Scholar

Copyright information

© Springer-Verlag London 2004

Authors and Affiliations

  • J. Žilinskas
    • 1
  • I. D. L. Bogle
    • 2
  1. 1.Faculty of InformaticsKaunas University of TechnologyKaunasLithuania
  2. 2.Centre for Process Systems Engineering, Department of Chemical EngineeringUniversity College LondonLondonUK

Personalised recommendations