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Inner estimation of solution sets of tied interval systems of linear equations
Dmitry Yuryevich Lyudvin

Institute of Computational Technologies SB RAS

UDC code: 519.67

This paper is devoted to the problem of inner estimation of united solution set of interval system of linear equations whose parameters are subject to additional ties. Adaptive partitioning of system’s parameters and methods of inner estimation based on formal and «center» approaches are proposed. The modification of «center» approach for inner estimation of solution set of tied interval linear system of equations with noninterval right-hand sides is developed. Results of numerical experiments are given.

Key Words
«center» approach, formal algebraic approach, inner estimation, solution set, interval linear systems

How to cite:
Lyudvin D. Y. Inner estimation of solution sets of tied interval systems of linear equations // Vestnik NSU Series: Information Technologies. - 2013. - Volume 11, Issue No 1. - P. 78-92. - ISSN 1818-7900. (in Russian).

Full Text in Russian

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1. Shary S. P. Resheniye intervalnykh lineinykh sistem so svyazyami // Sibirsky zhurnal vychislitelnoi matematiki. 2004. T. 7, № 4. S. 363376.
2. Alefeld G., Khertcberger Yu. Vvedeniye v intervalnyye vychisleniya. M.: Mir, 1987. 360 c.
3. Popova E. D. Explicit Description of AE Solution Sets for Parametric Linear Systems // SIAM J. Matrix Anal. Appl. 2012. Vol. 33. P. 1172–1189.
4. Dessombz O. Analysis of Mechanical Systems Using Interval Computations Applied to Finite Element Methods // J. of Sound and Vibration. 2001. Vol. 239. No. 5. P. 949968.
5. Jansson C. Interval Linear Systems with Symmetric, Skew-Symmetric Matrices and Dependencies in the Right Hand Side // Computing. 1991. Vol. 46. P. 265–274.
6. Muhanna R., Mullen R. Uncertainty in Mechanical Problems – Interval-Based Approach // J. Eng. Mech. 2001. Vol. 127. P. 557–566.
7. Kolev L. A Method for Outer Interval Solution of Linear Parametric Systems // Reliable Computing. 2004. Vol. 10. No. 3. P. 227239.
8. Popova E. D. Solving Linear Systems whose Input Data are Rational Functions of Interval Parameters // Preprint No. 3/2005. Institute of Mathematics and Informatics, BAS. Sofia, 2005.
9. Popova E., Krämer W. Inner and Outer Bounds for the Solution Set of Parametric Linear Systems // J. of Computational and Applied Mathematics. 2007. Vol. 199. P. 310–316.
10. Rump S. Verification Methods for Dense and Sparse Systems of Equations // Topics in Validated Numerics / Ed. by J. Herzberger. Amsterdam: Elsevier, 1994. P. 63135.
11. Skalna I. A Method for Outer Interval Solution of Systems of Linear Equations Depending Linearly on Interval Parameters // Reliable Computing. 2006. Vol. 12. No. 2. P. 107–120.
12. Shary S. P. Konechnomerny intervalny analiz. URL: interval/Library/InteBooks/SharyBook.pdf
13. Shary S. P. Algebraic Approach to the Interval Linear Static Identification, Tolerance and Control Problems, or One More Application of Kaucher Arithmetic // Reliable Computing. 1996. Vol. 2. No. 1. P. 3–33.
14. Alefeld G., Kreinovich V., Mayer G. On Symmetric Solution Sets // Computing Supplementum 16 / Ed. by J. Herzberger. Wien; N. Y.: Springer, 2003. P. 122.
15. Kaucher E. Algebraische Erweiterungen der Intervallrechnung unter Erhaltung Ordnungsund Verbandsstrukturen // Grundlagen der Computer-Arithmetic / Eds. R. Albrecht, U. Kulisch. Wien: Springer, 1977. P. 65–79.
16. Neumaier A. The Enclosure Solutions of Parameter-Dependent Systems of Equations // Reliability in Computing. 1988. Vol. 19. P. 269286.
17. Zholen L., Kifer M., Didri O., Valter E. Prikladnoi intervalny analiz. M.; Izhevsk, 2007. 468 s.
18. Shary S. P. Eshche raz o vnutrennem otcenivanii mnozhestv resheny intervalnykh lineinykh sistem // Vychislitelnyye tekhnologii. 2003. T. 8, spetc. vyp. S. 146–160.
19. Vasilyev F. P. Chislennyye metody resheniya ekstremalnykh zadach. M.: Nauka, 1988. 551 s.

Publication information
Main title Vestnik NSU Series: Information Technologies, Volume 11, Issue No 1 (2013).
Parallel title: Novosibirsk State University Journal of Information Technologies Volume 11, Issue No 1 (2013).

Key title: Vestnik Novosibirskogo gosudarstvennogo universiteta. Seriâ: Informacionnye tehnologii
Abbreviated key title: Vestn. Novosib. Gos. Univ., Ser.: Inf. Tehnol.
Variant title: Vestnik NGU. Seriâ: Informacionnye tehnologii

Year of Publication: 2013
ISSN: 1818-7900 (Print), ISSN 2410-0420 (Online)
Publisher: Novosibirsk State University Press
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