A Method for Calculating Interval Linear System

Volume 8, Issue 3, pp 193-204 http://dx.doi.org/10.22436/jmcs.08.03.02

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Authors

Shohreh Abolmasoumi - Department of Mathematics, Arak branch, Islamic Azad University, Arak, Iran. Majid Alavi - Department of Mathematics, Arak branch, Islamic Azad University, Arak, Iran.

Abstract

In this paper we represent an efficient algorithm for finding the interval solution for the interval linear system. This algorithm applies the optimization problem based on gradient vector in order to obtain the lower bound and upper bound of the interval solution.

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Keywords

• Interval number
• Interval linear system
• Interval matrix
• Cramer’s rule
• Gradient vector
• Multivariate function.

MSC

•  65F05
•  65F40
•  65G30

References

• [1] M. Alperbazaran, Calculation fuzzy inverse matrix using fuzzy linear equation system, Applied Soft Computing , 12 (2012), 1810-1813.
  • View Article
  • Google Scholar


• [2] G. Alefeld, J. Herzberger, Introduction to Interval Computations, Academic Press, New York (1983)
  • MathSciNet
  • Google Scholar


• [3] T. Allahviranloo, Successive over relaxation iterative method for fuzzy system of linear equation, Applied Mathematics and Computation , 162 (2005), 189–196.
  • View Article
  • MathSciNet
  • Google Scholar


• [4] M. Dehngan, B. Hashemi, Iterative solution of fuzzy linear systems, Applied Mathematics and Computation , 175 (2006), 645–674.
  • View Article
  • MathSciNet
  • Google Scholar


• [5] D. Dubois, H. Prade, Systems of linear fuzzy constraints, International Journal of Systems Science, 9 (1978), 613–626.


• [6] R. Fuller, Neural Fuzzy Systems , Donner visiting professor Abo Akademi university , ISBN 951-650-624-0, ISSN 0358-5654. (1395)
  • Google Scholar


• [7] K. Ganesan, P. Veeramani , On Arithmetic Operations of Interval Numbers, International Journal of Uncertainty, Fuzziness and Knowledge- Based Systems, 13 (6) (2005), 619 - 631.
  • View Article
  • MathSciNet
  • Google Scholar


• [8] K. Ganesan, On Some Properties of Interval Matrices, International Journal of Computational and Mathematical Sciences, 1 (2) (2007), 92-99.
  • MathSciNet
  • Google Scholar


• [9] S. Markov, Computation of algebraic solution to interval system via system of coordinates, Scientific computing, Validated Numerics, Interval methods, Eds. W. Kraemer, J. Wolff von Gudenberg, Kluwer, (2001), 103-114.
  • View Article
  • Google Scholar


• [10] E. Moor, R. Baker Kear foot, Michael.J. Cloud, Introduction to interval Analysis, (studies in Applied Mathematics, SILM , philaderphia,PA, USA, (1979), 19104 -2688
  • Google Scholar


• [11] Sukanta Nayak, S. Chakraverty, A new Approch to solve Fuzzy system of linear Equation, contents list available at tjmcs, journal of mathematics and computer science , 7 (2013), 205-212.
  • Google Scholar


• [12] S. H. Nasseri, F. Zahmatkesh, Huang method for solving full fuzzy linear system, The journal of Mathematics and Computer Science, 1 (2010), 1-5.
  • MathSciNet
  • Google Scholar


• [13] T. Nirmal, D. Datta, H. S. Kushwaha, K. Ganesan., Invers interval matrix: E new approach Applied Mathematics, Sciences, Vol.5, 201, no 13 (2011), 607-624.
  • MathSciNet
  • Google Scholar
  • MATH


• [14] E. R. Hansen, R. R. Smith, Interval arithmetic in matrix computations, Part 2, SIAM. Journal of Numerical Analysis, 4 (1967), 1 - 9.
  • View Article
  • MathSciNet
  • Google Scholar


• [15] D. S. Watkins, Fundamentals of Matrix Computations, Wiley-Interscience Pub., New York (2002)
  • Google Scholar