Solution sets for systems of linear interval equations

  • Zenon Kulpa Institute of Fundamental Technological Research Polish Academy of Sciences
  • Karol Rosłaniec Institute of Fundamental Technological Research Polish Academy of Sciences

Abstract

The paper discusses various classes of solution sets for linear interval systems of equations, and their properties. Interval methods constitute an important mathematical and computational tool for modelling real-world systems (especially mechanical) with (bounded) uncertainties of parameters, and for controlling rounding errors in computations. They are in principle much simpler than general probabilistic or fuzzy set formulation, while in the same time they conform very well with many practical situations. Linear interval systems constitute an important subclass of such interval models, still in the process of continuous development. Two important problems in this area are discussed in more detail- the classification of socalled united solution sets, and the problem of overestimation of interval enclosures (in the context of linear systems of equations called also a matrix coefficient dependence problem).

Keywords

References

[1] G. Alefeld, J. Herzberger. Introduction to Interval Computations. Academic Press, New York, 1983.
[2] G. Alefeld, V. Kreinovich, G. Mayer. The shape of the symmetric solution set. In: R.B. Kearfott, V. Kreinovich, eds., Applications of Interval Computations. Kluwer Academic Publishers, Dordrecht 1996.
[3] J.J. Buckley, Y. Qu. On using a-cuts to evaluate fuzzy equations. Fuzzy Sets and Systems, 38: 309- 312, 1990.
[4] E. Hansen. Global Optimization Using Interval Analysis. Marcel Dekker, New York, 1992.
[5] D.J. Hartfiel. Concerning the solution set of Ax = b where P :≤ A :≤ Q and p :≤ b :≤ q. Numerische Mathematik, 35: 355- 359, 1980.
Published
Mar 29, 2023
How to Cite
KULPA, Zenon; ROSŁANIEC, Karol. Solution sets for systems of linear interval equations. Computer Assisted Methods in Engineering and Science, [S.l.], v. 7, n. 4, p. 625-639, mar. 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1218>. Date accessed: 23 nov. 2024.
Section
Articles