Skip to main content
Log in

Inner estimation of the united solution set of interval linear algebraic system

Оценка цниз оэъединенного множества решений интервалъих линейнъих алгебраических систем

  • Mathematical Research
  • Published:
Reliable Computing

Abstract

It is shown that an algebraic interval solution of interval linear algebraic systems with matrix composed of “reverse” interval elements of the input matrix is a maximum inner estimation for the mited solution set in the sense of inclusion.

Abstract

Показано, пто алиебранчецкое ннтериалъное решенне интервальной линейной алгебраической системы матрина которой которои составлена из “инвептиронаиных” интервалов —алементов исхолной матрины является макснмалчной оненкой снизы лля обьелиненноо множестиа решений в цмысле нклочеиия.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Gardenes, E. andTrepat, A. Fundamentals of SIGLA, an interval computing system over the completed set of interoals. Computing24 (1980). pp. 161–179.

    MathSciNet  Google Scholar 

  2. Baucher, C. W. Interval analysis in the extended interval space Iℝ Computing Supplementum2 (1980), pp. 33–49.

    Google Scholar 

  3. Khlebalin, N. A. An analytical method for the synthesis of regulators under conditions of uncertainty in the plant’s parameters. In: “Analytical Methods for the Synthesis of Regulators Coll. of Scien. Proc.” Saratov Polytechnic Institute, Saratov, 1981. pp. 107–123 (in Russian).

    Google Scholar 

  4. Shary, S. P.,On some methods for solving the linear tolerance problem. Preprint 6, Computer Center, Siberian Branch of the USSR Academy of Sciences, Krasnoyarsk, 1989 (in Russian).

    Google Scholar 

  5. Shary, S. P. On compatibility of the linear tolerance problem. Interval Computation 1 (1991), pp. 92–98.

    Google Scholar 

  6. Shary, S. P. A new class of algorithms for optimal solution of interval linear systems. Interval Computations 4 (1992), pp. 18–29.

    MATH  MathSciNet  Google Scholar 

  7. Shary, S. P. Algebraic approach to the interval linear static identification, tolerance and control problems, or One more application of Kaucher arithmetic. Reliable Computing (1995), to appear.

  8. Zakharov, A. V. The solution of interval linear systems Ax=b and their properties. Dep. in VIMI 16.02.1989, N D007755 (in Russian).

  9. Zakharov, A. V. Constructing an interval algebraic solution in extended interval arithmetic. In: “Proc. All-Union Conf. on Actual Problems of Applied Mathematics, Saratov, May 20–22, 1991”, Saratov, 1991, pp. 311–317 (in Russian).

  10. Zakharov, A. V. andShokin, Yu. I. An algebraic interval solution for systems of algebraic equations Ax=b and Ax+d=b In: “Preprint 5, Computer Center, Siberian Branch of the USSR Academy of Sciences”, Krasnoyarsk, 1987, pp. 10–12 (in Russian).

    Google Scholar 

  11. Zyuzin, V. S. On a way of finding two-sided interval approximations for the solution of linear interval system of equations. In: “Diff. Equations and Functions Theory, Diff. Operatory i Voprosy Priblizheniya 7, Coll. of Sci. Proc.”, Saratov Univ., Saratov, 1987, pp. 28–32 (in Russian).

    Google Scholar 

  12. Zyuzin, V. S. An iterative method for solving a system of segment algebraic equations. In: “Diff. Equations and Functions Theory, Diff. Operatory i Voprosy Priblizheniya 8, Coll. of Sci. Proc.”, Saratov Univ., Saratov, 1989. pp. 72–82 (in Russian).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kupriyanova, L., КуПиянова, А. Inner estimation of the united solution set of interval linear algebraic system. Reliable Comput 1, 15–31 (1995). https://doi.org/10.1007/BF02390519

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02390519

Keywords

Navigation